BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Differentiation-invariant subspaces of $\\Omega$-ultradifferentia ble functions for which weak spectral synthesis fails DTSTART;VALUE=DATE-TIME:20241126T121000Z DTEND;VALUE=DATE-TIME:20241126T124500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-746@indico.eimi.ru DESCRIPTION:Speakers: Natalia Abuzyarova (Institute of Mathematics with Co mputing Centre of RAS\, Ufa)\nWe consider a spectral synthesis problem for differentiation-invariant subspaces in a general space $\\mathcal E_{\\Om ega} (a\;b)$ of $\\Omega$-ultradifferentiable functions\, where \n$(a\;b)\ \subseteq\\mathbb R $ and $\\Omega=\\{\\omega_n\\}$ is a sequence of nonq uasianalytic weights subjected some standard restrictions of $\\Omega$-ult radifferentiable functions theory.\nDo there exist differentiation-invari ant subspaces $W\\subset\\mathcal E_{\\Omega} (a\;b)$ for which weak spe ctral synthesis fails?\nAlexandru Aleman\, Anton Baranov and Yurii Belov c onstructed the first example of differentiation-invariant subspace in $C^{ \\infty}(a\;b)$ which does not admit weak spectral synthesis (2015).\nWe a nswer the above question using a dual scheme. Namely\, we consider a topo logical module $P=\\mathcal F(\\mathcal E'_{\\Omega} (a\;b))$\, where $\\m athcal F$ denotes the Fourier-Laplace transform\, and find $unlocalisable$ primary submodules $J\\subset P$. Then\, the differentiation-invariant su bspaces in $\\mathcal E_{\\Omega} (a\;b)$ which dual submodules are $J$ d o not admit the weak spectral synthesis.\n\nhttps://indico.eimi.ru/event/1 671/contributions/746/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/746/ END:VEVENT BEGIN:VEVENT SUMMARY:Random walk on dynamical percolation: separating critical and supe rcritical regimes (online) DTSTART;VALUE=DATE-TIME:20241125T080000Z DTEND;VALUE=DATE-TIME:20241125T090000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-735@indico.eimi.ru DESCRIPTION:Speakers: Yuval Peres (Beijing institute of Mathematical Scien ces and Applications (BIMSA))\nIn Dynamical Percolation each edge is open with probability $p$\, refreshing its status at rate $r>0$. This process w as introduced in the 1990s by Haggstrom\, Steif and the speaker\, motivate d by a question of Malliavin. Remarkable results on exceptional times in t wo dimensions were obtained by Schramm\, Steif\, Garban and Pete.\n\nWe st udy random walk on dynamical percolation in the lattice $Z^d$\, where the walk moves along open edges at rate 1. \n\nLet $p_c=p_c(d)$ denote the cr itical value for static percolation. In the critical regime $p=p_c$\, we prove that if $d=2$ or $d>10$\, then the mean squared displacement is $O(t r^a)$ where $a=a(d)>0$. For $p>p_c$\, we prove that the mean squared d isplacement is of order $t$\, uniformly in $0\n\nhttps://indico.eimi.ru/e vent/1671/contributions/735/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/735/ END:VEVENT BEGIN:VEVENT SUMMARY:Математическое моделирование и пер сонализированная медицина в современно й клинической практике DTSTART;VALUE=DATE-TIME:20241128T130000Z DTEND;VALUE=DATE-TIME:20241128T133500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-763@indico.eimi.ru DESCRIPTION:Speakers: Tatyana Vavilova (Almazov National Medical Research Centre & Saint Petersburg State University)\nTBA\n\nhttps://indico.eimi.ru /event/1671/contributions/763/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/763/ END:VEVENT BEGIN:VEVENT SUMMARY:Color transformations for medical video images DTSTART;VALUE=DATE-TIME:20241129T075500Z DTEND;VALUE=DATE-TIME:20241129T084000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-766@indico.eimi.ru DESCRIPTION:Speakers: Natalia Obukhova (Saint Petersburg Electrotechnical University «LETI»)\nThe existing methods of color transformations synthe sizing for medical video systems are discussed. The main problems of their application are identified. It is shown that the existing approaches\, so lving private problems\, lead to the general inconsistency of color transf ormations in the medical video systems. A new quality criterion for the co lor transformations synthesis taking into account both the accuracy of col or rendering and the transmission of local color contrast is proposed. Exa mples of synthesis of color transformations for target tasks of endoscopic image processing using the proposed criterion are considered.\n\nhttps:// indico.eimi.ru/event/1671/contributions/766/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/766/ END:VEVENT BEGIN:VEVENT SUMMARY:Системный анализ факторов\, влияющи х на течение вирусного поражения легких (на примере НКИ). DTSTART;VALUE=DATE-TIME:20241129T142400Z DTEND;VALUE=DATE-TIME:20241129T144500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-797@indico.eimi.ru DESCRIPTION:Speakers: Е.С. Вдоушкина (Самара)\nhttps://in dico.eimi.ru/event/1671/contributions/797/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/797/ END:VEVENT BEGIN:VEVENT SUMMARY:Вопросы нечеткой логики в вопросах диагностики туберкулезной инфекции. DTSTART;VALUE=DATE-TIME:20241129T140300Z DTEND;VALUE=DATE-TIME:20241129T142400Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-796@indico.eimi.ru DESCRIPTION:Speakers: Е.А. Амосова (Самара)\nhttps://indico .eimi.ru/event/1671/contributions/796/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/796/ END:VEVENT BEGIN:VEVENT SUMMARY:Перспективы использования "диагнос тических метрик" для повышения эффектив ности скрининга заболеваний легких. DTSTART;VALUE=DATE-TIME:20241129T134200Z DTEND;VALUE=DATE-TIME:20241129T140300Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-795@indico.eimi.ru DESCRIPTION:Speakers: Ю.Т. Гогоберидзе (Самара)\, Е.А . Бородулина (Самара)\, И.А. Просвиркин (Са мара)\, Б.Б. Бородулин (Самара)\, Е.И. Поваля ев (Самара)\nhttps://indico.eimi.ru/event/1671/contributions/795/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/795/ END:VEVENT BEGIN:VEVENT SUMMARY:Система поддержки принятия врачебн ых решений при лечении туберкулеза. DTSTART;VALUE=DATE-TIME:20241129T132100Z DTEND;VALUE=DATE-TIME:20241129T134200Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-794@indico.eimi.ru DESCRIPTION:Speakers: Е.А. Бородулина (Самара)\, Е.П. Еременко (Самара)\nhttps://indico.eimi.ru/event/1671/contrib utions/794/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/794/ END:VEVENT BEGIN:VEVENT SUMMARY:Математическое моделирование в про гнозе распространения туберкулезной ин фекции в РФ. DTSTART;VALUE=DATE-TIME:20241129T130000Z DTEND;VALUE=DATE-TIME:20241129T132100Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-793@indico.eimi.ru DESCRIPTION:Speakers: А.А. Старшинова (Санкт-Петерб ург)\, Н.Н. Осипов (Санкт-Петербург)\, А.Я. К ульпина (Санкт-Петербург)\, Е.Н. Беляева ( Санкт-Петербург)\nhttps://indico.eimi.ru/event/1671/contribu tions/793/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/793/ END:VEVENT BEGIN:VEVENT SUMMARY:Применение нейросетевого алгоритма в дифференциальной диагностике кольпос копической картины. DTSTART;VALUE=DATE-TIME:20241129T123800Z DTEND;VALUE=DATE-TIME:20241129T130000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-792@indico.eimi.ru DESCRIPTION:Speakers: И.Е. Говоров (Санкт-Петербург )\, Е.А. Ульрих (Санкт-Петербург)\nhttps://indico.ei mi.ru/event/1671/contributions/792/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/792/ END:VEVENT BEGIN:VEVENT SUMMARY:Валидация шкалы SCORE-2 на выборке из р оссийской популяции. DTSTART;VALUE=DATE-TIME:20241129T121500Z DTEND;VALUE=DATE-TIME:20241129T123800Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-791@indico.eimi.ru DESCRIPTION:Speakers: В.А. Куценко (Москва)\, Г.Е. Сви нин (Москва)\, А.Э. Имаева (Москва)\nhttps://indico .eimi.ru/event/1671/contributions/791/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/791/ END:VEVENT BEGIN:VEVENT SUMMARY:Специализированные информационные решения Акросс - Клиническая лаборатори я (АКЛ). Модуль Бактериология. DTSTART;VALUE=DATE-TIME:20241129T115300Z DTEND;VALUE=DATE-TIME:20241129T121500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-790@indico.eimi.ru DESCRIPTION:Speakers: Н.М. Захаров (Москва)\nhttps://indico .eimi.ru/event/1671/contributions/790/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/790/ END:VEVENT BEGIN:VEVENT SUMMARY:Анализ данных и машинное обучение д ля эффективной диагностики и лечения со циально значимых заболеваний. DTSTART;VALUE=DATE-TIME:20241129T113000Z DTEND;VALUE=DATE-TIME:20241129T115300Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-789@indico.eimi.ru DESCRIPTION:Speakers: Н.Н. Осипов (Санкт-Петербург)\ , Д.М. Спельников (Санкт-Петербург)\nhttps://ind ico.eimi.ru/event/1671/contributions/789/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/789/ END:VEVENT BEGIN:VEVENT SUMMARY:DiaCompanion. Прогнозирование постпранди альной гликемии у беременных женщин с ге стационным сахарным диабетом в мобильно м приложении. DTSTART;VALUE=DATE-TIME:20241129T094800Z DTEND;VALUE=DATE-TIME:20241129T100000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-788@indico.eimi.ru DESCRIPTION:Speakers: А.Д. Анопова (Санкт-Петербург )\, А.О. Исаков (Санкт-Петербург)\nhttps://indico.ei mi.ru/event/1671/contributions/788/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/788/ END:VEVENT BEGIN:VEVENT SUMMARY:Предикторы развития венозных тромб оэмболических осложнений у пациентов с глиальными опухолями ЦНС: возможности р азличных алгоритмов. DTSTART;VALUE=DATE-TIME:20241129T093600Z DTEND;VALUE=DATE-TIME:20241129T094800Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-787@indico.eimi.ru DESCRIPTION:Speakers: К.А. Пищулов (Санкт-Петербург )\, О.М. Моисеева (Санкт-Петербург)\, М.А. Си макова (Санкт-Петербург)\, Т.В. Вавилова (С анкт-Петербург)\nhttps://indico.eimi.ru/event/1671/contributi ons/787/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/787/ END:VEVENT BEGIN:VEVENT SUMMARY:Применение искусственного интеллек та в разработке способа прогнозирования восстановления овуляции у женщин с синд ромом поликистозных яичников. DTSTART;VALUE=DATE-TIME:20241129T092400Z DTEND;VALUE=DATE-TIME:20241129T093600Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-786@indico.eimi.ru DESCRIPTION:Speakers: Е.А. Васюкова (Санкт-Петербу рг)\, А.О. Исаков (Санкт-Петербург)\, Е.К. За йкова (Санкт-Петербург)\, А.И. Ерисковская (Санкт-Петербург)\, П.В. Попова (Санкт-Пет ербург)\nhttps://indico.eimi.ru/event/1671/contributions/786/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/786/ END:VEVENT BEGIN:VEVENT SUMMARY:Шкалы риска венозных тромбозов у па циентов с солидными опухолями. DTSTART;VALUE=DATE-TIME:20241129T091200Z DTEND;VALUE=DATE-TIME:20241129T092400Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-785@indico.eimi.ru DESCRIPTION:Speakers: М.А. Овчинникова (Санкт-Петер бург)\, В.С. Власов (Санкт-Петербург)\nhttps://i ndico.eimi.ru/event/1671/contributions/785/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/785/ END:VEVENT BEGIN:VEVENT SUMMARY:Математическое моделирование для о пределения диагностически значимых имм унологических показателей при дифферен циальной диагностике туберкулеза и сарк оидоза. DTSTART;VALUE=DATE-TIME:20241129T090000Z DTEND;VALUE=DATE-TIME:20241129T091200Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-784@indico.eimi.ru DESCRIPTION:Speakers: А.А. Рубинштейн (Санкт-Петерб ург)\, И.В. Кудрявцев (Санкт-Петербург)\, Д. М. Спельников (Санкт-Петербург)\, Н.Н. Осип ов (Санкт-Петербург)\, А.А\, Старшинова (Са нкт-Петербург)\nhttps://indico.eimi.ru/event/1671/contribution s/784/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/784/ END:VEVENT BEGIN:VEVENT SUMMARY:Искусственный интеллект как инстру мент поиска неспецифических признаков п ри проведении диагностических исследов аний у пациентов с сердечно-сосудистыми заболеваниями. DTSTART;VALUE=DATE-TIME:20241129T081500Z DTEND;VALUE=DATE-TIME:20241129T084500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-783@indico.eimi.ru DESCRIPTION:Speakers: Д.И. Курапеев (Санкт-Петербур г)\nhttps://indico.eimi.ru/event/1671/contributions/783/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/783/ END:VEVENT BEGIN:VEVENT SUMMARY:Машинное обучение в медицине: преим ущества и недостатки. DTSTART;VALUE=DATE-TIME:20241129T074500Z DTEND;VALUE=DATE-TIME:20241129T081500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-782@indico.eimi.ru DESCRIPTION:Speakers: В.А. Мулюха (Санкт-Петербург)\ nhttps://indico.eimi.ru/event/1671/contributions/782/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/782/ END:VEVENT BEGIN:VEVENT SUMMARY:Особенности правовой охраны средст в индивидуализации в медицине. DTSTART;VALUE=DATE-TIME:20241129T070000Z DTEND;VALUE=DATE-TIME:20241129T073000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-781@indico.eimi.ru DESCRIPTION:Speakers: М.В. Дышлюк (Санкт-Петербург)\ nhttps://indico.eimi.ru/event/1671/contributions/781/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/781/ END:VEVENT BEGIN:VEVENT SUMMARY:Стратегия правовой защиты разработ ок для надежной защиты интеллектуальной собственности и повышения инвестиционн ой привлекательности. DTSTART;VALUE=DATE-TIME:20241129T063000Z DTEND;VALUE=DATE-TIME:20241129T070000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-780@indico.eimi.ru DESCRIPTION:Speakers: Т.Н. Эриванцева (Москва)\nhttps:// indico.eimi.ru/event/1671/contributions/780/ LOCATION:СПбГУ МКН Аудитория 301 URL:https://indico.eimi.ru/event/1671/contributions/780/ END:VEVENT BEGIN:VEVENT SUMMARY:On integrability of majorants of Fourier sums DTSTART;VALUE=DATE-TIME:20241130T074500Z DTEND;VALUE=DATE-TIME:20241130T082000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-773@indico.eimi.ru DESCRIPTION:Speakers: Nikolai Antonov (N.N. Krasovskii Institute of Mathem atics and Mechanics\, Ekaterinburg)\nLet $\\varphi \\colon \\ [0\,+\\infty ) \\to\n[0\,+\\infty )$ be a nondecreasing function\, $\\omega $ be an ar bitrary modulus of continuity. Denote by $\\varphi (L)$ the set of all $2\ \pi$-periodic Lebesgue measurable functions $f$ such that\n$\\varphi (|f|) $ is summable on $[0\, 2\\pi )$\, and by $H_1^{\\omega}$ the set of all $f \\in L$ whose $L^1$-modulus of continuity $\\omega (f\, \\delta )_1$ sati sfies the condition $\\omega (f\,\\delta )_1 = O(\\omega (\\delta ))$.\n\n Suppose that $f \\in L(\\mathbb{T} )$\, denote by $S_n(f\,x)$ the $n$th pa rtial sum of the trigonometric Fourier series ($n$th Fourier sum) of $f$\, and by\n$$\nM(f\,x)= \\sup \\limits _{n \\ge 1} |S_n(f\,x) |\n$$\nthe maj orant of the Fourier sums of $f$. We consider the problems of conditions f or the almost everywhere convergence of the Fourier series and the integra bility of the majorant of the Fourier sums of $f$ in terms of the belongin g of this function to classes $\\varphi (L)$ and $H_1^{\\omega}$. We pro pose to discuss multidimensional analogs of these problems for the case of rectangular partial sums of multiple trigonometric Fourier series.\n\nhtt ps://indico.eimi.ru/event/1671/contributions/773/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/773/ END:VEVENT BEGIN:VEVENT SUMMARY:Fekete lemma in Banach spaces (online) DTSTART;VALUE=DATE-TIME:20241127T135000Z DTEND;VALUE=DATE-TIME:20241127T142500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-756@indico.eimi.ru DESCRIPTION:Speakers: Aleksei Kulikov (University of Copenhagen\, Denmark )\nThe classical Fekete lemma says that if the sequence of real numbers $a _n$ satisfies the inequality $a_{n+m}\\le a_n + a_m$ for all $n\, m\\in \\ mathbb{N}$ then the limit $\\lim_{n\\to \\infty} \\frac{a_n}{n}$ exists. I n this talk we will discuss what happens when $a_n$ are the elements of so me Banach space. The main result that we will discuss is the following the orem.\n\n\n$Theorem$. Let $X$ be a uniformly convex Banach space and let $a_n$ be a sequence of vectors in $X$ such that $||a_{n+m}|| \\le ||a_n+a_ m||$ for all $n\, m\\in \\mathbb{N}$. Then the limit $\\lim_{n\\to \\infty } \\frac{a_n}{n}$ exists.\n\n\nInterestingly\, the condition of uniform co nvexity is essential -- if $X$ is not convex (that is\, if the unit sphere of $X$ contains an interval) then it is not hard to see that the Fekete l emma fails\, but even for convex\, but not uniformly convex spaces there m ight be a counterexample.\n\nThe talk is based on a joint work with Feng S hao.\n\nhttps://indico.eimi.ru/event/1671/contributions/756/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/756/ END:VEVENT BEGIN:VEVENT SUMMARY:Residue techniques in the study of Euler--Mellin integrals DTSTART;VALUE=DATE-TIME:20241127T121000Z DTEND;VALUE=DATE-TIME:20241127T124500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-754@indico.eimi.ru DESCRIPTION:Speakers: Irina Antipova (Siberian Federal University\, Krasno yarsk)\nThe main objects of the theory of multidimensional residues are in tegrals of rational $n$-forms over $n$-dimensional cycles lying in the com plement of a polar hypersurface in affine\, projective\, and toric spaces. Developing ideas of F. Griffiths\, V. Batyrev proved (1993) that all peri ods are $A$-hypergeometric functions in the sense of I. Gelfand\, M. Kapra nov and A. Zelevinsky (1990) if the differential form is considered by var ying all parameters. The Batyrev class can be significantly expanded by mo ving from integer parameters to complex ones\, and instead of compact homo logy in integration\, we can consider cycles with closed (unbounded) suppo rts. Such a generalization can be achieved by considering Mellin transform s in the class of branching integrals (Euler--Mellin integrals). In the la st decade\, particular interest has arisen in the study of such integrals in connection with the study of Feynman integrals in quantum field theory and string amplitudes in superstring theory. In Bayesian statistics\, such integrals appear as marginal likelihood integrals.\n\nThe convergence of the Euler--Mellin integral is ensured by the property of quasi-ellipticity of the integrand denominator\, first introduced by T. Ermolaeva and A. Ts ikh (1996). In the talk we are going to discuss representations of the Eul er--Mellin integrals associated with facets of the Newton polytope of the denominator\, and their treatments in the context of the theory of Feynma n integrals.\n\nhttps://indico.eimi.ru/event/1671/contributions/754/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/754/ END:VEVENT BEGIN:VEVENT SUMMARY:Generalization of the Rossovskii problem on the limit of a special product of sines DTSTART;VALUE=DATE-TIME:20241126T143000Z DTEND;VALUE=DATE-TIME:20241126T150500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-749@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Sherstyukov (Lomonosov Moscow State Univers ity)\nSome time ago\, in the theory of functional differential equations w ith affine transformations\, the problem of calculating the spectral radiu s for a certain parametric family of operators arose.\nThe question comes down to finding the limit of the special product of sines with arguments g enerated by a given geometric progression. The report plans to discuss a m ore general problem in which an arbitrary infinitely large sequence is tak en as the generating sequence.\n\nhttps://indico.eimi.ru/event/1671/contri butions/749/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/749/ END:VEVENT BEGIN:VEVENT SUMMARY:Random unconditional convergence of Rademacher chaos in $L_\\infty $ and its applications to graph theory DTSTART;VALUE=DATE-TIME:20241126T100500Z DTEND;VALUE=DATE-TIME:20241126T104000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-745@indico.eimi.ru DESCRIPTION:Speakers: Sergei Astashkin (Samara National Research Universit y)\, Konstantin Lykov (Institute of Mathematics of the National Academy of Sciences of Belarus)\nAccording a recent result due to the authors of thi s talk\, both multiple Rademacher system and Rademacher chaos possess the property of random unconditional convergence in $L_\\infty$. This fact c ombined with some novel connections between $L_\\infty$-norms of linear co mbinations of elements of these systems and some special norms of matrices of their coefficients allows us to establish sharp two-sided estimates fo r the discrepancy of weighted graphs and hypergraphs. Some of these result s extend the classical theorems proved by Erdös and Spencer for the unwei ghted case.\n\nhttps://indico.eimi.ru/event/1671/contributions/745/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/745/ END:VEVENT BEGIN:VEVENT SUMMARY:Density of homogeneous polynomials (online) DTSTART;VALUE=DATE-TIME:20241126T091000Z DTEND;VALUE=DATE-TIME:20241126T095500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-744@indico.eimi.ru DESCRIPTION:Speakers: András Kroó (Alfréd Rényi Institute of Mathemati cs\, Budapest)\nIn this talk we will consider the following central proble m on the uniform approximation by homogeneous polynomials:\n\nFor which 0- symmetric star like domains $K\\subset \\mathbb R^d$ and which $f\\in C(\\ partial K)$ there exist homogeneous polynomials $h_{n}\, h_{n+1}$ of degre e $n$ and $n+1$\, respectively\, so that uniformly on $\\partial K$\n$$f= \\lim_{n\\rightarrow \\infty}(h_{n}+h_{n+1})? $$\nThis is the analogue of the classical Weierstrass approximation problem with polynomials of total degree being replaced by homogeneous polynomials.\nThe answer to the above problem has an intrinsic connection to the geometry of the underlying dom ain. We will give a survey of various results related to the above questio n and will also list some important open problems.\n\nhttps://indico.eimi. ru/event/1671/contributions/744/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/744/ END:VEVENT BEGIN:VEVENT SUMMARY:Low-rank approximation analysis DTSTART;VALUE=DATE-TIME:20241126T070000Z DTEND;VALUE=DATE-TIME:20241126T074500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-742@indico.eimi.ru DESCRIPTION:Speakers: Eugene Tyrtyshnikov (Marchuk Institute of Numerical Mathematics of RAS\, Moscow)\nTensor decompositions become a very popular tool for modelling data in many application problems. However\, a better u nderstanding of why they are so efficient is still a hot issue with a mach inery based on some relevant probability models for data. We discuss some open questions and new developments \nof cross-approximation approach to optimization problems with the tensor-train model.\n\nReferences:\n\n1. $E . Tyrtyshnikov$\,\nTensor decompositions and rank increment conjecture\, R ussian Journal of Numerical Analysis and Mathematical Modelling\, 25 (4)\, 239--246 (2020).\n\n2. $D. Zheltkov\, E. Tyrtyshnikov$\,\nGlobal optimiza tion based on TT-decomposition\, Russian Journal of Numerical Analysis and Mathematical Modelling\, 25 (4)\, 247--261 (2020).\n\nhttps://indico.eimi .ru/event/1671/contributions/742/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/742/ END:VEVENT BEGIN:VEVENT SUMMARY:On reverse Markov--Nikol'skii inequalities for polynomials with ze ros on a segment DTSTART;VALUE=DATE-TIME:20241125T144000Z DTEND;VALUE=DATE-TIME:20241125T151500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-741@indico.eimi.ru DESCRIPTION:Speakers: Mikhail Komarov (Vladimir State University)\nLet $\\ Pi_n$ be the class of algebraic polynomials $P$ of degree $n$\, all of who se zeros lie on the segment $[-1\,1]$.\nIn 1995\, S.P. Zhou has proved the following Turán type\nreverse Markov--Nikol'skii inequality:\n$$\\|P'\\| _{L_p[-1\,1]}>c\\\, {(\\sqrt{n})}^{1-1/p+1/q}\\\, \\|P\\|_{L_q[-1\,1]}\, P \\in \\Pi_n\,$$\nwhere $ 0 < p \\le q \\le \\infty\, 1-1/p+1/q \\ge 0 $ ($ c>0$ is a constant independent of $P$ and $n$).\nWe show that Zhou's estim ate remains true in the case $p=\\infty$\, $q>1$. Some of related Turán t ype inequalities are also discussed.\n\nhttps://indico.eimi.ru/event/1671/ contributions/741/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/741/ END:VEVENT BEGIN:VEVENT SUMMARY:The method for solving the Delsarte problem for designs on homogen eous spaces DTSTART;VALUE=DATE-TIME:20241125T140000Z DTEND;VALUE=DATE-TIME:20241125T143500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-740@indico.eimi.ru DESCRIPTION:Speakers: Dmitry Gorbachev (Tula State University\, St. Peters burg State University)\nWe study the problem of finding lower bounds for t he cardinality of weighted designs on compact rank-1 spaces. To solve this problem\, P. Delsarte\, J. Goethals\, and J. Seidel introduced what is kn own as the linear programming bound\, based on a two-point distribution of the design. This bound is based on solving an extremal problem known as t he Delsarte problem for Jacobi--Fourier series. Earlier\, V.V. Arestov\, A .G. Babenko\, and their students proposed a solution scheme for a similar problem in the case of spherical codes\, based on the primal-dual problem. We adapt this scheme to the case of designs. The scheme is based on conve x analysis and consists of several steps\, including: formulating the dual problem for the Stieltjes measure\, proving the existence of an extremal function and measure\, deriving duality relations\, characterizing extrema l functions and measures based on these relations\, reducing the problem t o a polynomial system of equations in specific cases\, proving the existen ce of an analytical solution to the system through its certification or by using a special Gröbner basis\, and applying the uniform Stieltjes--Bern stein estimate.\nThe described method has been used to solve several new D elsarte problems. These results are useful in the problem of integral norm discretization when estimating the number of nodes in discrete norms.\n\n https://indico.eimi.ru/event/1671/contributions/740/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/740/ END:VEVENT BEGIN:VEVENT SUMMARY:Constructive recovery of values of an algebraic function via Hermi te--Padé polynomials DTSTART;VALUE=DATE-TIME:20241125T122000Z DTEND;VALUE=DATE-TIME:20241125T125500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-738@indico.eimi.ru DESCRIPTION:Speakers: Aleksandr Komlov (Steklov Mathematical Institute of RAS\, Moscow)\nLet $f$ be an algebraic function of degree $m+1$ and $f_\\i nfty$ be its holomorphic germ at the point $\\infty$. Hermite--Padé polyn omials of type I for the tuple $[1\,f_\\infty\,f_\\infty^2\, \\dots\,f_\\i nfty^m]$ of order $n$ at $\\infty$ are $m+1$ polynomials $Q_{n\,j}$\, $j=0 \,\\dots\,m$\, such that $\\deg Q_{n\,j}\\le n$ and\n$$\nQ_{n\,0}(z)+Q_{n\ ,1}(z)f_\\infty(z)+Q_{n\,2}(z)f_\\infty^2(z)+\\dots+Q_{n\,m}(z)f_\\infty^m (z)=O(z^{-m(n+1)}) \n$$\nas $z\\to\\infty$.\n\nIn 1984 J. Nuttall (not in general case and not with full proofs) and in 2017 E. Chirka\, R. Palvelev \, S. Suetin and A. Komlov (in general case and with full proofs) showed t hat $Q_{n\,m-1}/Q_{n\,m}$ asymptotically recover the sum of the values of $f$ on first $m$ sheets of Nuttall partition of the Riemann surface of $f$ . So\, this ratio recovers sum of $m$ values of $(m+1)$-valued function $f $.\n\nIn 2021 the polynomial Hermite--Padé $m$-system was introduced. Wit h the help of this system we show that for generic function $f$ the ratio of some minors of size $m+1-k$ of the $(m+1)\\times(m+1)$ matrix consistin g of Hermite--Padé polynomials of order $n\, n-1\,\\dots\, n-m$ asymptoti cally recover the sum of the values of $f$ on first $k$ sheets of Nuttall partition of the Riemann surface of $f$ for each $k=1\,\\dots\,m$. Hence w e constructivelly recover $m$ values of $(m+1)$-valued algebraic function $f$.\n\nhttps://indico.eimi.ru/event/1671/contributions/738/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/738/ END:VEVENT BEGIN:VEVENT SUMMARY:Average Kolmogorov width and its applications DTSTART;VALUE=DATE-TIME:20241129T091000Z DTEND;VALUE=DATE-TIME:20241129T094500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-778@indico.eimi.ru DESCRIPTION:Speakers: Yuri Malykhin (Steklov Mathematical Institute of RAS \, Moscow)\nThe classical notion of Kolmogorov width of a set in a normed space measures the error of approximation of this set by n-dimensional lin ear subspaces. Here we consider the ''worst-case'' error of approximation. \n \nIf we take the ''average-case'' error instead\, we arrive to the noti on of average Kolmogorov width. We will discuss some new bounds for the av erage widths and some applications for the classical Kolmogorov widths.\n\ nhttps://indico.eimi.ru/event/1671/contributions/778/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/778/ END:VEVENT BEGIN:VEVENT SUMMARY:Approximation by simplest fractions and simplest bianalytic sums DTSTART;VALUE=DATE-TIME:20241130T122500Z DTEND;VALUE=DATE-TIME:20241130T130000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-777@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Fedorovskiy (Lomonosov Moscow State Unive rsity and Saint Petersburg State University)\nWe will discuss the question on approximation by simplest fractions (i.e.\, sums of Cauchy kernels wit h unit coefficients) and by simplest bianalytic sums (i.e.\, sums of funda mental solutions to the Bitsadze equation with unit coefficients). We will start with Chui's conjecture and its version for weighted (Hilbert) Bergm an spaces. For a wide class of weights\, it will be shown that for every $ N$\, the simplest\nfractions with $N$ poles on the unit circle have minima l norm if and only if the poles are equidistributed on the circle. Next\, we describe the closure of the simplest fractions in weighted Bergman spac es under consideration. These results were obtained at 2021 in the joint w ork by the speaker with E.~Abakumov (Univ. Gustave Eiffel\, Paris\, France ) and A.~Borichev (Aix–Marseille University\, France). Finally\,\nwe discuss the problem on approximation of functions by simplest bianalytic fractions\,and several new effects and phenomena that appeared in this con nection. This part is based on the joint work in progress by the speaker w ith P.~Borodin (Lomonosov Moscow State University).\n\nhttps://indico.eimi .ru/event/1671/contributions/777/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/777/ END:VEVENT BEGIN:VEVENT SUMMARY:The length conjecture for hyperbolic knot complements DTSTART;VALUE=DATE-TIME:20241130T114000Z DTEND;VALUE=DATE-TIME:20241130T121500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-776@indico.eimi.ru DESCRIPTION:Speakers: Mauricio Romo (Shanghai Institute for Mathematics an d Interdisciplinary Sciences (SIMIS) and Fudan University)\nI will explain a conjecture that relates the asymptotics of the colored Jones polynomial s for links with the geodesic length of certain loops inside hyperbolic kn ot complements. If time allows I will give a physics motivation for this c onjecture based on SL(2\,C) Chern-Simons theory.\n\nhttps://indico.eimi.ru /event/1671/contributions/776/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/776/ END:VEVENT BEGIN:VEVENT SUMMARY:Automorphisms of Hopf manifolds of dimension $n\\geq2$ DTSTART;VALUE=DATE-TIME:20241130T093500Z DTEND;VALUE=DATE-TIME:20241130T101000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-775@indico.eimi.ru DESCRIPTION:Speakers: Elijah Lopatin (Steklov Mathematical Institute of RA S\, Moscow)\nDescribing the group of automorphisms $\\mathrm{Aut}(X)$ of a compact complex manifold $X$ is among the classical issues of complex geo metry. According to the Bochner--Montgomery~[1] theorem\, such groups are complex Lie groups and it is almost everything we can a priori say about t hem: for a majority of $X$\, it is extremely complicated (or nearly imposs ible) to find the generating set of $\\mathrm{Aut}(X)$ or some other expli cit characterisation.\n\nTherefore it is natural to investigate classifica tion properties\, i.e. such properties that the group $\\mathrm{Aut}(X)$ p ossesses one when $X$ is a complex manifold\, and does not for other $X$. It seems the Jordan property~[8] to be the most promising. \n\nLet $G$ be a group. We say that $G$ is \\textit{Jordan} (or has the \\textit{Jord an property}) if there is a constant $J = J(G)\\in\\mathbb N$ such that fo r any finite subgroup $H\\subset G$ there is a normal abelian subgroup $A \\unlhd H$ of index at most $J(G)$. \n\nIt is known that automorphism grou ps of complex projective varieties~[5] and\, more generally\, compact KГ ¤hler manifolds~[7]\nare Jordan. For non-KГ¤hler compact complex manifo lds there are only a few known results on the Jordan property for automorp hism groups: for compact complex manifolds in Fujiki's class $\\mathcal{C} $~[6]\, for compact complex surfaces~[9] and for some examples~[3\,4] of n on-KГ¤hler holomorphically symplectic manifolds~[2].\n\nHopf manifold $\ \mathsf{H}_n$\, i.\\\,e. a compact complex manifold of dimension $n\\geq 2 $ such that its universal cover is isomorphic to $\\mathbb C^n\\setminus 0 $\, is a natural example of non-KГ¤hler complex manifold for studying st ructural properties of its automorphism group. $\\mathsf{H}_n$ is realized as a quotient of $\\mathbb{C}^n\\setminus0$ by a free action of a group i somorphic to $\\mathbb Z$\, which acts on $\\mathbb{C}^n\\setminus0$ via b iholomorphic contractions $\\mathbb C^n\\setminus 0\\to\\mathbb C^n\\setmi nus 0$. Recently it was shown~[10] that $\\mathrm{Aut}(\\mathsf{H}_n)$ is Jordan. We expand on the results of~[10] proving that the group $\\mathrm{ Aut}(\\mathsf{H}_n)/\\mathrm{Aut}^0(\\mathsf{H}_n)$ is finite\; here $\\ma thrm{Aut}^0(\\mathsf{H}_n)$ is the connected component of unity in $\\math rm{Aut}(\\mathsf{H}_n)$. We also provide the explicit structure of mention ed biholomorphic contractions. \n\nThis is a joint research with Constant in Shramov\, Steklov Mathematical Institute of RAS\, Moscow.\n\n\\begin{ce nter}\n \\textbf{References}\\\\[.3cm]\n\\end{center}\n\n\\begin{enumera te}\n\\item\nBochner\, S. and Montgomery\, D. \\textit{Groups on analytic manifolds\,} Annals of Mathematics \\textbf{48}\, (1947)\, 659--669.\n\n\\ item \nBogomolov\, F.\, Kurnosov\, N.\, Kuznetsova\, A. and Yasinsky\, E. \\textit{Geometry and automorphisms of non-KГ¤hler holomorphic symplecti c manifolds\,} Int. Math. Res. Notices IMRN 2022:6\, 12302--12341.\n\n\\it em\n Guan\, D. \\textit{Examples of compact holomorphic symplectic manifol ds which are not KГ¤hlerian. II\,} Inventiones Mathematicae \\textbf{121 }:1\, (1995)\, 135--145.\n\n\\item \nGuan\, D. \\textit{Examples of compac t holomorphic symplectic manifolds which are not KГ¤hlerian. II\,} Inter nat. J. Math. \\textbf{6}:5\, (1995)\, 709--718.\n\n\\item Meng\, S. and Z hang\, D.-Q. \\textit{Jordan property for nonlinear algebraic groups and p rojective varieties\,} Amer. J. Math. \\textbf{140}:4\, (2018)\, 1133--114 5.\n\n \\item\n Meng\, S.\, Perroni\, F. and Zhang\, D.-Q. \\textit{Jorda n property for automorphism groups of compact spaces in Fujiki’s cla ss $\\mathcal{C}$\,} J. Topol. \\textbf{15}:2\, (2022)\, 806--814.\n \n \ \item \nKim\, J.\\\, H. \\textit{Jordan property and automorphism groups o f normal compact KГ¤hler varieties\,} Commun. Contemp. Math. \\textbf{20 }:3\, (2018)\, 1750024. \n\n\\item \nPopov\, V.\\\,L. \\textit{On the Mak ar-Limanov\, Derksen invariants\, and finite automorphism groups of algebr aic varieties}\, in: \\textit{Affine Algebraic Geometry: The Russell Fests chrift\,} CRM Proceedings and Lecture Notes\, Vol. 54\, Amer. Math. Soc.\, 2011\, pp. 289--311. \n\n\\item\nProkhorov\, Yu. and Shramov\, C. \\texti t{Automorphism groups of compact complex surfaces\,} Int. Math. Res. Notic es \\textbf{2021}:14\, (2021)\, 10490--10520.\n\n\\item Savelyeva\, A. \\t extit{Automorphisms of Hopf manifolds\,} Journal of Algebra \\textbf{638}\ , (2024)\, 670--681. \n\n\\end{enumerate}\n\nhttps://indico.eimi.ru/event /1671/contributions/775/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/775/ END:VEVENT BEGIN:VEVENT SUMMARY:Integral potential type operator for infinitely differentiable and real analytic functions DTSTART;VALUE=DATE-TIME:20241130T085000Z DTEND;VALUE=DATE-TIME:20241130T092500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-774@indico.eimi.ru DESCRIPTION:Speakers: Simona Myslivets (Siberian Federal University\, Kras noyarsk)\nWe prove the infinite differentiability of an integral operator of the potential type for an infinitely differentiable function defined on the boundary of the domain in $\\mathbb{C}^n$ with the boundary of the cl ass $\\mathcal{C}^\\infty$\, up to the boundary of the domain on both side s.\n\nWe also prove the real analyticity of the Bochner--Martinelli integr al for a real analytic function given at the boundary of the domain.\n\n\n The author was supported by the Krasnoyarsk Mathematical Center and financ ed by the Ministry of Science and Higher Education of the Russian Federati on in the framework of the establishment and development of regional Cente rs for Mathematics Research and Education (Agreement No. 075-02-2020-1534/ 1).\n\nhttps://indico.eimi.ru/event/1671/contributions/774/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/774/ END:VEVENT BEGIN:VEVENT SUMMARY:Extremal measures and asymptotics of orthogonal polynomials of a d iscrete variable DTSTART;VALUE=DATE-TIME:20241130T070000Z DTEND;VALUE=DATE-TIME:20241130T073500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-772@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Lysov (Keldysh Institute of Applied Mathema tics of RAS\, Moscow)\nIn the series of works of the 1980s\, A.A. Gonchar and E.A. Rakhmanov developed a method for studying the asymptotic behavio r of polynomials orthogonal with respect to varying (i.e.\, depending on t he degree of the polynomial) weight. \nOrthogonality was considered both o n real intervals and on curves with special symmetry ($S$-property).\nWe e xtend these results in two directions. \nFirst\, we consider multiple orth ogonality\, and second\, discrete orthogonality measures. \nDuring the tal k we formulate some general results and provide specific examples of their use.\n\nhttps://indico.eimi.ru/event/1671/contributions/772/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/772/ END:VEVENT BEGIN:VEVENT SUMMARY:Stability of min- and max-approximation DTSTART;VALUE=DATE-TIME:20241129T143000Z DTEND;VALUE=DATE-TIME:20241129T150500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-771@indico.eimi.ru DESCRIPTION:Speakers: Alexey Alimov (Lomonosov Moscow State University and Saint Petersburg State University)\nApproximative compactness type proper ties in min- and max-approximation are studied. Problems of this kind le ad in a~natural way to ''special points'' of approximation theory\, viz.\ , the spaces characterized in terms of approximative compactness for vari ous problems of approximation. On this way\, there appear CLUR-spaces\, Da y--Oshman spaces\, Anderson--Megginson spaces\, and CMLUR- and AT-spaces.\ n\nhttps://indico.eimi.ru/event/1671/contributions/771/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/771/ END:VEVENT BEGIN:VEVENT SUMMARY:Analytic extension of simple and multiple power series by means of coefficients interpolation DTSTART;VALUE=DATE-TIME:20241129T125000Z DTEND;VALUE=DATE-TIME:20241129T132500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-770@indico.eimi.ru DESCRIPTION:Speakers: Alexandr Mkrtchyan (Siberian Federal University\, Kr asnoyarsk\, and Institute of Mathematics NAS RA)\nOne of the methods of s tudying the problem of analytical continuation of power series is interpol ation of the coefficients of the series.\nWith this approach \nLe Roy and Lindelöf obtained conditions under which a series analytically extends into a sector. Note that the theorem\, gave a connection between the sect or and the growth of the interpolation function. More precisely\, the type of interpolation function must be less than $\\pi$ on the closed half-pl ane $Re z \\geq 0$.\n \nWe weakened the condition of less than $\\pi$ on t he fact that the sum of the indicator (growth) on directions $\\frac{\\pi} {2}$ and $-\\frac{\\pi}{2}$ is less than $2\\pi$. \nAlso we obtain the mul tivariate version of this theorem\, i.e. establish a connection between th e growth of the interpolating function of the coefficients on the imagina ry subspace and the multivariate sectoral domain where the multiple series is analytically extends.\n\nhttps://indico.eimi.ru/event/1671/contributio ns/770/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/770/ END:VEVENT BEGIN:VEVENT SUMMARY:Maximal operators on spaces BMO and BLO DTSTART;VALUE=DATE-TIME:20241129T121000Z DTEND;VALUE=DATE-TIME:20241129T124500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-769@indico.eimi.ru DESCRIPTION:Speakers: Grigori Karagulyan (Yerevan State University and Ins titute of Mathematics of National Academy of Sciences of RA)\nWe consider maximal kernel-operators on measure spaces $(X\,\\mu)$ equipped with a bal l-basis. We prove that under certain asymptotic condition on the kernels t hose operators maps boundedly $\\text{BMO(X)}$ into $\\text{BLO(X)}$\, gen eralizing the well-known results of Bennett--DeVore--Sharpley and Bennett for the Hardy--Littlewood maximal function. As a particular case of such an operator one can consider the maximal function \n$$\\mathcal{M}_{\\phi} f(x)=\\sup_{r>0}\\frac{1}{r^d}\\int_{\\mathbb{R}^d}|f(t)|\\phi\\left(\\fr ac{x-t}{r}\\right)dt\,$$\nand its non-tangential version\, where $\\phi(x) \\ge 0$ is a bounded\, integrable spherical function on $\\mathbb{R}^d$\, decreasing with respect to $|x|$. We prove that $\\mathcal{M}_\\phi$ is b ounded from $\\text{BMO}(\\mathbb{R}^d)$ to $\\text{BLO}(\\mathbb{R}^d)$ i f and only if \n$$\\int_{\\mathbb{R}^d}\\phi(x)\\log (2+|x|)dx\n\nhttps:// indico.eimi.ru/event/1671/contributions/769/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/769/ END:VEVENT BEGIN:VEVENT SUMMARY:Holomorphic self-maps of a disc with fixed points DTSTART;VALUE=DATE-TIME:20241129T095500Z DTEND;VALUE=DATE-TIME:20241129T103000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-768@indico.eimi.ru DESCRIPTION:Speakers: Olga Kudryavtseva (Lomonosov Moscow State University and Saint Petersburg State University)\, Aleksei Solodov (Lomonosov Mosco w State University and Saint Petersburg State University)\nFixed points of a holomorphic self-map of the unit disc have a decisive influence on its geometric and analytic properties. In the talk\, we give an overview of kn own and new results on classes of such functions. The presentation focuses on approaches to solving extremal problems on classes of functions with s everal fixed points.\n\nhttps://indico.eimi.ru/event/1671/contributions/76 8/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/768/ END:VEVENT BEGIN:VEVENT SUMMARY:Approximation of locally-constant functions by algebraic polynomia ls and some applications DTSTART;VALUE=DATE-TIME:20241129T135000Z DTEND;VALUE=DATE-TIME:20241129T142500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-767@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Ryutin (Lomonosov Moscow State University and Moscow Center of Fundamental and Applied Mathematics)\, Yuri Malykhi n (Steklov Mathematical Institute of RAS\, Moscow)\nWe plan to talk about explicit explicit easily implementable polynomial approximations of suffi ciently high accuracy for locally constant functions on the union of disj oint segments and some more general disjoint sets. \n\nThis problem has i mportant applications in several areas of numerical analysis\, complexity theory\, quantum algorithms\, etc. The one\, most relevant for us\, is t he amplification of approximation method: it allows to construct approxima tions of higher degree $M$ and better accuracy from the approximations\nof degree $m$. Such constructions are used in linear algebra\, computer sci ence (communication complexity).\n\nhttps://indico.eimi.ru/event/1671/cont ributions/767/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/767/ END:VEVENT BEGIN:VEVENT SUMMARY:Discrete models for differentially constrained spaces DTSTART;VALUE=DATE-TIME:20241129T070000Z DTEND;VALUE=DATE-TIME:20241129T074500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-765@indico.eimi.ru DESCRIPTION:Speakers: Dmitriy Stolyarov (Saint Petersburg State University and St. Petersburg Department of Steklov Institute of Mathematics)\nI wil l speak about a mysterious correspondence between inequalities for special discrete time martingales and solutions to certain PDEs. Usually these in equalities involve the~$L_1$ norms of functions and martingales and\, thus \, have applications to geometric measure theory. The said correspondence also works for questions in geometric measure theory (quantifying singular ities of martingales and singularities of PDE solutions). It seems that th ere are much more questions than answers here.\n\nhttps://indico.eimi.ru/e vent/1671/contributions/765/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/765/ END:VEVENT BEGIN:VEVENT SUMMARY:Hyperbolic Fourier series and the Klein--Gordon equation DTSTART;VALUE=DATE-TIME:20241128T140000Z DTEND;VALUE=DATE-TIME:20241128T150000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-764@indico.eimi.ru DESCRIPTION:Speakers: Haakan Hedenmalm (Royal Institute of Technology (KTH )\, Stockholm\, and Saint Petersburg State University)\nThe Klein--Gordon equation in 1+1 dimensions is one of the truly basic second order PDEs wit h constant coefficients.\nIt models the time evolution of a one-dimensiona l relativistic boson with spin 0. Since it is relativisitic\, the tempora l relation between points is felt\, and a given pair of points is either t ime-like or space-like. If the pair of points is space-like\, we cannot sa y that one or the other event happens before or after the other. \nIf we s tudy a space-like cone\, and place equidistributed points on the edges\, d o we get a uniqueness set for Klein--Gordon solutions? \nThe answer turns out to depend on the density of points\, and the shape of the solution.\n\ nAs a consequence\, we are led to study hyperbolic Fourier series\, a topi c which is natural but is a recent discovery only. The first installment i s a paper with A. Montes-Rodriguez (Annals of Mathematics\, 2011). The sec ond only exists as\na 2024 preprint\, but it builds on insights in the wor k of Radchenko and Viazovska (2019).\n\nhttps://indico.eimi.ru/event/1671/ contributions/764/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/764/ END:VEVENT BEGIN:VEVENT SUMMARY:Coefficientwise total positivity of some matrices defined by linea r recurrences DTSTART;VALUE=DATE-TIME:20241128T122000Z DTEND;VALUE=DATE-TIME:20241128T125500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-762@indico.eimi.ru DESCRIPTION:Speakers: Alexandr Dyachenko (Keldysh Institute of Applied Mat hematics of RAS\, Moscow)\nA matrix of polynomials is called coefficientwi se totally positive (CTP)\nif all its minors are polynomials with positive coefficients. We verify\nthis property for a few families of infinite low er-triangular matrices.\nDuring the talk we will\, in particular\, touch u pon CTP triangular\nmatrices stemming from orthogonal and multiple orthogo nal polynomials.\n\nIt is also intriguing to consider triangles generated by other types of\nrecurrence relations. Almost 30 years ago Brenti conjec tured that the\nEulerian triangle (the lower-triangular matrix of Eulerian numbers\,\nA008292 in OEIS) is totally positive. The Eulerian numbers app ear in\npolylogarithms of negative integer orders and count the number of\ npermutations of $1\,2\,...\,n+1$ with $k$ excedances. We introduce a more \ngeneral family of matrices that experimentally appear to be CTP. Then we \nprove that its special subfamily including the reversed Stirling subset\ ntriangle (A008278) is indeed CTP. This result is new and required a more\ ndelicate approach\, than total positivity in the non-reversed case (cf.\n A008277 in OEIS).\n\nhttps://indico.eimi.ru/event/1671/contributions/762/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/762/ END:VEVENT BEGIN:VEVENT SUMMARY:Uniqueness theorems for holomorphic functions in the unit disk and completeness of various systems of functions DTSTART;VALUE=DATE-TIME:20241128T095500Z DTEND;VALUE=DATE-TIME:20241128T103000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-761@indico.eimi.ru DESCRIPTION:Speakers: Bulat Khabibullin (Institute of Mathematics with Com puting Centre of RAS\, Ufa)\nWe present new uniqueness theorems for holomo rphic functions in the unit disk with given subharmonic majorants for the logarithms of the modules of these holomorphic functions. The results are formulated in terms of zero distributions of these holomorphic functions and Riesz mass distributions of these subharmonic majorants. \nThey take into account the distributions of zeros and masses both by radius and by a rgument. We also present applications of these uniqueness theorems to ques tions of completeness of various systems of holomorphic functions in weigh t spaces of holomorphic functions. The research was supported by a grant f rom the Russian Science Foundation No. 24-21-00002.\n\nhttps://indico.eimi .ru/event/1671/contributions/761/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/761/ END:VEVENT BEGIN:VEVENT SUMMARY:On embedding theorems for function spaces with mixed logarithmic s moothness DTSTART;VALUE=DATE-TIME:20241128T091000Z DTEND;VALUE=DATE-TIME:20241128T094500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-760@indico.eimi.ru DESCRIPTION:Speakers: Gabdolla Akishev (Kazakhstan Branch of Lomonosov Mos cow State University\, Astana)\nThe talk discusses the Lorentz space $L_{p \, \\tau}(\\mathbb{T}^{m})$\, $2\\pi$ periodic functions of many variables and $S_{p\, \\theta}^{0\, \\overline{ b}}\\mathbf{B}$\, $S_{p\, \\theta} ^{0\, \\overline{b}}B$ --- spaces with mixed logarithmic smoothness\, equi valent norms of spaces with mixed logarithmic smoothness\, necessary and s ufficient conditions for the embedding of spaces $S_{p\, \\theta}^{0\, \\o verline{b}}\\mathbf{B}$\, $S_{p\, \\theta}^{0\, \\overline{b}}B$ into each other.\n\nhttps://indico.eimi.ru/event/1671/contributions/760/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/760/ END:VEVENT BEGIN:VEVENT SUMMARY:Singularity of random Bernoulli matrices DTSTART;VALUE=DATE-TIME:20241128T075500Z DTEND;VALUE=DATE-TIME:20241128T084000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-759@indico.eimi.ru DESCRIPTION:Speakers: Alexander Litvak (University of Alberta\, Edmonton\, Canada)\nWe discuss recent progress on singularity of random matrices wit h i.i.d. 0/1 Bernoulli entries. \nThis talk is partially based on a joint work with K. Tikhomirov.\n\nhttps://indico.eimi.ru/event/1671/contribution s/759/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/759/ END:VEVENT BEGIN:VEVENT SUMMARY:$K$-theory of graded $C^*$-algebras in the tight-binding model of solid state theory DTSTART;VALUE=DATE-TIME:20241128T070000Z DTEND;VALUE=DATE-TIME:20241128T074500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-758@indico.eimi.ru DESCRIPTION:Speakers: Armen Sergeev (Steklov Mathematical Institute\, Mosc ow & Saint Petersburg State University)\nAfter the discovery of quantum Ha ll effect and its topological explanation the mathematical methods based o n the theory of $C^*$-algebras and their K-theory enter firmly into the ar senal of solid state physics.\n\nA key role in the theory of solid states is played by their symmetry groups. It was Kitaev who has pointed out the relation between the symmetries of solid bodies and Clifford algebras.\n\n In this talk we pay main attention to the class of solid bodies called the topological insulators. They are characterized by having a broad energy g ap stable under small deformations. The algebras of observables of such so lid bodies belong to the class of graded $C^*$-algebras for which there is a variant of K-theory proposed by Van Daele. It makes possible to define the topological invariants of insulators in K-theory terms.\n\nhttps://ind ico.eimi.ru/event/1671/contributions/758/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/758/ END:VEVENT BEGIN:VEVENT SUMMARY:Factorization representation and properties of zero sets of some w eighted classes of analytic functions in the unit disk DTSTART;VALUE=DATE-TIME:20241127T143000Z DTEND;VALUE=DATE-TIME:20241127T150500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-757@indico.eimi.ru DESCRIPTION:Speakers: Faizo Shamoyan (Saratov State University)\nIn the ta lk we consider the problem the factorization of certain classes of analyti c functions in the unit disk\, for which the logarithm of modulus belongs to the weighted $L^p$ classes.\n\nhttps://indico.eimi.ru/event/1671/contri butions/757/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/757/ END:VEVENT BEGIN:VEVENT SUMMARY:Generalizations of Bernstein and Videnskii operators DTSTART;VALUE=DATE-TIME:20241127T100500Z DTEND;VALUE=DATE-TIME:20241127T104000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-755@indico.eimi.ru DESCRIPTION:Speakers: Alexey Lukashov (Moscow Institute of Physics and Tec hnology)\nBernstein operators are associated with Bernoulli scheme as foll ows: $$B_n(f\,x)=\\mathbb{E}\\left(f\\circ Z(n\,x)\\right)\,$$ where $Z(n\ ,x)=\\frac{1}{n}\\sum_{i=1}^n Y(i\,x)\,$ $Y(i\,x)$ is the sequence of inde pendent Bernoulli random variables with parameters $P\\{Y(i\,x)=1\\}=x$ an d $P\\{Y(i\,x)=0\\}=1-x.$ V.S. Videnskii in a series of papers studied gen eralizations of Bernstein operators to the case of rational functions. The y can be written in the form $$V_n(f\,x)=\\mathbb{E}\\left(f\\circ(\\mathb b{E}Z(n\,x))^{-1}\\circ Z(n\,x)\\right)\,$$ where $Y(i\,n)$ has now parame ters $p_{in}(x)=\\frac{\\rho_{in}x}{1+\\rho_{in}-x}\,$ $ \\rho_{i\,n}>0\, $ instead of $x.$\nWe give a survey of results to compare approximation pr operties of Bernstein and Videnskii type generalizations for one or sever al intervals\, and for the semi-axis.\n\nhttps://indico.eimi.ru/event/1671 /contributions/755/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/755/ END:VEVENT BEGIN:VEVENT SUMMARY:On the power of adaption\, randomization and non-linear measuremen ts (online) DTSTART;VALUE=DATE-TIME:20241127T125000Z DTEND;VALUE=DATE-TIME:20241127T132500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-753@indico.eimi.ru DESCRIPTION:Speakers: Mario Ullrich (Johannes Kepler University\, Linz\, A ustria)\nWe show that the maximal gain of adaption and randomization is li mited when considering approximation of functions from convex sets based o n arbitrary linear measurements in a worst-case setting. \nWe also discuss the situation when arbitrary non-linear\, Lipschitz-continuous measuremen ts are allowed\, where some (surprising) improvements hold.\n\nhttps://ind ico.eimi.ru/event/1671/contributions/753/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/753/ END:VEVENT BEGIN:VEVENT SUMMARY:To Birman--Krein--Vishik theory of nonnegative symmetric operators with compact preresolvent DTSTART;VALUE=DATE-TIME:20241127T091000Z DTEND;VALUE=DATE-TIME:20241127T095500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-752@indico.eimi.ru DESCRIPTION:Speakers: Mark Malamud (Saint Petersburg State University)\nLe t $A\\ge 0$ be a closed densely defined non-negative symmetric operator i n a Hilbert space ${\\frak H}$\, let ${\\frak H}_1 := \\text{ran}(A+I)$\, and let $P_1$ be the orthoprojection in $\\frak H$ onto $\\frak H_1$.\ nLet also $A_{F}$ and $A_{K}$ be\, respectively\, the maximal (Friedrichs ') and minimal (Krein's) non-negative selfadjoint extensions of $A$.\nNex t\, assuming $A$ to be positive definite\, $A \\ge m_A > 0$\, Krein chara cterized the extension $A_K$ as follows:\n\n$$\\text{dom} A_K = \\text{dom } A + {\\frak N}_0\,\\\,\\text{where}\\\, {\\frak N}_0 = \\text{ker}A*.$$\ n\nTherefore Krein's extension $A_{K}$ admits the following representatio n:\n\n$$A_K = A'_K \\oplus (O | {\\frak N}_0)\,$$ \n\nwhere $$A'_{K} := A_K | {\\frak M}_0\, \\text{ and } {\\frak M}_0 := {\\frak N}_0^{\\perp} = \\text{ran} A$$. \nThe operator $ A_{K}'$ is called the reduced Krein extension. We will discuss relations between certain spectral properties o f the operators $A_{F}\, A_{K}'$ and $A$ assuming the operator $(A +I)^{- 1}$ to be compact. First we discuss the validity of the following equiv alence:\n\n$$\nP_1 (I_{\\frak H} + A)^{-1} \\in \\frak S(\\frak H_1) \\qu ad \\Longleftrightarrow \\quad (I_{{\\frak M}_0} + A'_K)^{-1}\n\\in \\f rak S(\\frak M_0 )\,\n $$\n\nwhich improves and complements the known Krei n's result.\nHere $\\frak S$ is arbitrary symmetrically normed ideal $\\f rak S$ including Neumann-Schatten ideals $\\frak S = \\frak S_{p}$\, $p\\i n (0\,\\infty]$\, as well as ideals $\\Sigma_p$ (a compact operator $T$ is put in the class $\\Sigma_p(\\frak H)\,$ if $s_n(T))= O(n^{-1/p})\, p\ \in(0\,\\infty)$).\n\nSecondary we will discuss the improvement of above e quivalence for $\\frak S = \\Sigma_p$. It happens that the inclusion $P_1 (I_{\\frak H} + A)^{-1} \\in \\Sigma_p(\\frak H_1)$ for some $p\\in(0\,\ \infty)$ does not ensure coincidence of the eigenvalues asymptotics of ope rators\, i.e. the following equivalence with some $a\\ge 0:$\n\n\n$$\n\\l ambda_n\\bigl(P_1(I_{\\frak H} + A)^{-1}\\bigr) = an^{-1/p}\\left(1 +\no( 1)\\right)\\quad \\Longleftrightarrow \\quad \\lambda_n \\bigl((I_{{\\fra k M}_0} + \\widehat A'_K)^{-1}\\bigr)\n= a n^{-1/p}\\left(1 + o(1)\\right) .\n$$\n\n\nIn fact\, it will be explained that the validity of this equiv alence as $n\\to \\infty$ depends on $A_F$.\n\nWe will also discuss the a bstract Alonso-Simon problem [1] on the eigenvalues asymptotics of $A_{F }$ and $A_{K}'$\,\nand the explicit solution to the Birman problem.\n\nBes ides\, we discuss improvement of Birman's and Grubb's results (see [2]\, [ 3]) regarding equivalence of semiboundedness\nproperties of an extension $\\widetilde A = \\widetilde A^*$ of $A$ and the corresponding boundary op erator.\n\n\nA part of results of the talk are announced in [4] and pub lished in [5].\n$$\\\,$$\nReferences:\n$$\\\,$$\n1. $A. Alonso\, B. Simon $\, The Birman-Krein-Vishik theory of self-adjoint extensions of semib ounded operators\, J. Operator Theory\, 4 (1980)\, 251--270. $$\\\,$$ \n\n2. $M.S. Birman$\, On the self-adjoint extension s of positive definite operators\, Mat. Sb.\, 38\, 431--450 (1956). \n$$\\\,$$\n3. $G. Grubb$ \, A characterization of the non-local boundary value problems associate d with an elliptic operator\, Ann. Scuola Norm. Sup. Pisa (3)\, 22 (1968) \, 425--513. \n$$\\\, $$\n4. $M.M. Malamud$\, To Birman--Krein--Vishik theory\, Doklady Mathema tics\, 10\, No.1 (2023)\, 44--48. \n$$\\\,$$\n5. $M.M. Malamud$\, Explicit solution to the Birman problem for the $2D$-Laplace operator\, Russian Journal of Math ematical Physics\, 31\, No. 3 (2024)\, 495--503.\n\nhttps://indico.eimi.r u/event/1671/contributions/752/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/752/ END:VEVENT BEGIN:VEVENT SUMMARY:Effective approximation of high-dimensional probability distributi ons DTSTART;VALUE=DATE-TIME:20241127T075500Z DTEND;VALUE=DATE-TIME:20241127T084000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-751@indico.eimi.ru DESCRIPTION:Speakers: Ivan Oseledets (Skolkovo Institute of Science and Te chnology\, Moscow)\nIn this talk\, I will discuss recent advances and chal lenges in the approximation of high-dimensional probability \ndistribution s\, knowing only its samples $x_1\, \\ldots\, x_n$.\nSuch problems appear in many applications. I will discuss techniques such as normalising flows\ , diffusion models and flow matching.\n\nhttps://indico.eimi.ru/event/167 1/contributions/751/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/751/ END:VEVENT BEGIN:VEVENT SUMMARY:Random sampling discretization of integral norms in finite-dimensi onal spaces (online) DTSTART;VALUE=DATE-TIME:20241127T070000Z DTEND;VALUE=DATE-TIME:20241127T074500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-750@indico.eimi.ru DESCRIPTION:Speakers: Feng Dai (University of Alberta\, Edmonton\, Canada) \nIn this talk\, I will present recent advancements in the Marcinkiewicz d iscretization problem using random sampling in finite-dimensional spaces . The goal is to establish two-sided estimates for the integral norm of functions in the space via a finite sum of function values evaluated at randomly selected points that are independent of the individual functi ons in the space. The main challenge is to determine the ''nearly'' optima l number of random points required for the Marcinkiewicz discretization in equalities to hold with high probability.\n\nhttps://indico.eimi.ru/event/ 1671/contributions/750/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/750/ END:VEVENT BEGIN:VEVENT SUMMARY:On the wavelet transform of periodic ultradifferentiable functions DTSTART;VALUE=DATE-TIME:20241126T135000Z DTEND;VALUE=DATE-TIME:20241126T142500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-748@indico.eimi.ru DESCRIPTION:Speakers: Ildar Musin (Institute of Mathematics with Computing Centre of RAS\, Ufa)\nThe main part of the talk is devoted to wavelet tra nsform on the space of periodic ultradifferentiable functions of Roumieu t ype. \nIt is based on recent results on Gelfand--Shilov spaces and descrip tion of periodic ultradifferentiable functions of Roumieu type in terms of decay of their Fourier coefficients.\n\nhttps://indico.eimi.ru/event/1671 /contributions/748/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/748/ END:VEVENT BEGIN:VEVENT SUMMARY:Multishift in a Hilbert space DTSTART;VALUE=DATE-TIME:20241126T125000Z DTEND;VALUE=DATE-TIME:20241126T132500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-747@indico.eimi.ru DESCRIPTION:Speakers: Pavel Terekhin (Saratov State University)\nTBA\n\nht tps://indico.eimi.ru/event/1671/contributions/747/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/747/ END:VEVENT BEGIN:VEVENT SUMMARY:Infinite-dimensional conic Steiner formula DTSTART;VALUE=DATE-TIME:20241126T075500Z DTEND;VALUE=DATE-TIME:20241126T084000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-743@indico.eimi.ru DESCRIPTION:Speakers: Dmitry Zaporozhets (St. Petersburg Department of Ste klov Institute of Mathematics)\nThe classical Steiner formula expresses th e volume of the neighborhood of a convex compact set in $\\mathbb{R}^d$ as a polynomial in the radius of the neighborhood. In the work of Tsirelson (1985)\, this result was extended to the infinite-dimensional case. A sphe rical analogue of the Steiner formula for convex subsets of $\\mathbb{S}^{ d-1}$ is also well-known. Using Tsirelson's idea of applying the theory of Gaussian processes\, we obtain an infinite-dimensional version of this sp herical analogue.\n\nThe talk is based on a joint work with Maria Dospolov a.\n\nhttps://indico.eimi.ru/event/1671/contributions/743/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/743/ END:VEVENT BEGIN:VEVENT SUMMARY:Inequalities for quasinorms of rational functions in a domain and on its boundary DTSTART;VALUE=DATE-TIME:20241125T130000Z DTEND;VALUE=DATE-TIME:20241125T133500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-739@indico.eimi.ru DESCRIPTION:Speakers: Tatsiana Mardvilko (Belarusian State University\, Mi nsk)\nPreviously (in 2011)\, the author together with A.A. Pekarski obtain ed an inequality connecting the quasinorms of rational functions with resp ect to the linear measure on $\\mathbb{R}$ and the planar measure in the h alf-plane $\\Pi=\\{z\\in\\mathbb{C}:\\Im z>0\\}$. In this context\, the ra tional functions belonged to the weighted Lebesgue space in $\\Pi$\, where the quasinorm is defined as follows \n$$\n\\|f\\|_{L_{p\,\\mu}(\\Pi)}=\\l eft(\\int_{\\Pi}(\\Im z)^{p\\mu-1}|f(z)|^p\\\,dm_2(z)\\right)^{1/p}\,\\qua d p>0\,\\quad \\mu>0.\n$$\n Here $m_2$ is the planar Lebesgue measure in $\\mathbb{C}$.\n\nThe report will discuss some applications of the noted i nequality. Furthermore\, a generalization of this inequality for a domain whose boundary is a Lavrent'ev curve will be presented.\n\nhttps://indico. eimi.ru/event/1671/contributions/739/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/739/ END:VEVENT BEGIN:VEVENT SUMMARY:On distributed optimization problems under similarity: optimal alg orithms and fast extensions DTSTART;VALUE=DATE-TIME:20241125T100500Z DTEND;VALUE=DATE-TIME:20241125T105000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-737@indico.eimi.ru DESCRIPTION:Speakers: Alexander Beznosikov (Moscow Institute of Physics an d Technology)\, Alexander Gasnikov (Innopolis University and Steklov Mathe matical Institute\, Moscow)\nIn this talk\, we consider distributed method s for solving optimization problems. In the distributed formulation\, the target function is divided into parts\, and each of these parts can be acc essed only by a local agent/worker. We deal with the case where the local functions are ''similar'' to each other in some sense. Due to the ''simila rity'' it is possible to achieve a significant acceleration of the theoret ical guarantees of convergence of methods in terms of estimates on communi cation complexity. Besides the issue of convergence of algorithms and obta ining upper bounds\, we touch upon lower complexity bounds and verify the optimality of the proposed methods. In the remaining time\, we try to disc uss the question of how we can ''break through'' the lower estimates and c onstruct an even faster method\, in particular\, we additionally introduce the possibility of compressing the transmitted information\, modify the p roposed algorithms and obtain upper and lower bounds in a new formulation. \n\nhttps://indico.eimi.ru/event/1671/contributions/737/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/737/ END:VEVENT BEGIN:VEVENT SUMMARY:Normal random matrices and recurrence relations for multiple orth ogonal polynomials DTSTART;VALUE=DATE-TIME:20241125T091000Z DTEND;VALUE=DATE-TIME:20241125T095500Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-736@indico.eimi.ru DESCRIPTION:Speakers: Alexander Aptekarev (Keldysh Institute of Applied Ma thematics of RAS)\nOur main attention will be devoted to the normal matric es ensembles\, which have many interesting applications (Laplacian growth\ , Diffusion limited aggregation). An important feature of the orthogonal p olynomials ensembles of random matrices is that the joint probability dens ity of their eigenvalues is represented by means of the determinants compo sed by Christoffel--Darboux (CD) kernels of orthogonal polynomials or the ir generalizations. For the normal matrices ensembles the corresponded CD kernel is taken for polynomials orthogonal with respect to an area measure . We show that for some special cases of the normal random matrices (relat ed with discrete Painlevé equation) these polynomials are the multiple or thogonal polynomials. This fact makes their asymptotical analysis much eas ier.\n\nhttps://indico.eimi.ru/event/1671/contributions/736/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/736/ END:VEVENT BEGIN:VEVENT SUMMARY:Opening of the conference DTSTART;VALUE=DATE-TIME:20241125T075000Z DTEND;VALUE=DATE-TIME:20241125T080000Z DTSTAMP;VALUE=DATE-TIME:20260615T232714Z UID:indico-contribution-1671-734@indico.eimi.ru DESCRIPTION:https://indico.eimi.ru/event/1671/contributions/734/ LOCATION:Saint-Petersburg University URL:https://indico.eimi.ru/event/1671/contributions/734/ END:VEVENT END:VCALENDAR