Young Researchers' Seminar

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  • Casey Blacker

Young Researchers' Seminar

venue SPbU, Dept. of Mathematics & Computer Science
Room 201
time biweekly, Friday 12:50 – 1:40
organizer  Casey Blacker (cblacker271@gmail.com)

The aim of this seminar is to provide a forum for young researchers to share their interests and showcase their results. Expository talks by senior faculty and academic visitors are also welcome.

Lunch will be provided. If you plan to attend, please indicate your lunch preferences here: https://public.eimi.ru/~cblacker/pizza.html
 

Oct   1 Ivan Telpukhovskiy
Geometry of Teichmüller space
I will give a quick overview of the geometry of Teichmüller space with various metrics on it. In the end I will mention some open problems.
15  Olga Parshina
A few words on combinatorics
I'll cover some problems arising in combinatorial study of symbolic sequences.
29 Boris Zolotov
Dynamic explicit Voronoi diagrams
I'll extend on my struggles to create sublinear algorithms that maintain the explicitly stored graph of a Voronoi diagram under insertion of a new point.
Nov 12 Konstantin Kalinin
Viscous fingers and mixing zone growth rate estimates
We will consider a system of PDEs that describes miscible displacement in porous media. If the initial and boundary conditions are such that a more viscous fluid displaces a less viscous fluid, their interface is unstable. Any small perturbation leads to viscous fingers. In practice, the following question plays an important role: is it possible to estimate the velocity of the fingers? Time permitting, we will talk about the applications of these estimates in the optimal injection profile problem.
26 Dmitrii Adler
Jacobi forms and root systems
In 1992 K. Wirthmuller proved an analogue of the Chevalley theorem for weak Jacobi forms associated with irreducible root systems, except $E_8$. However, generators in his proof are not constructed explicitly, but they are important in applications. In my talk, I will discuss the new simple approach to this problem in cases of root systems D_n and F_4. Following this method, it is possible to construct the generators of the corresponding algebras of weak Jacobi forms using only Jacobi theta functions and modular differential operators.
Dec 10 Casey Blacker
Hamiltonian manifolds and generalizations
In the first part of this talk, I will introduce foundational concepts in the theory of Hamiltonian manifolds, including symplectic manifolds, moment maps, and reduction. Following this, I will discuss extensions of these ideas to more general settings, such as multisymplectic and generalized complex manifolds.
24 Rahul Gangopadhyay
Crossings in geometric hypergraphs
We introduce the notion of a geometric hypergraph. We discuss the extremal result in the geometric hypergraph, i.e., how many hyperedges a uniform geometric hypergraph can have if it does not contain any crossing pair of hyperedges? We then discuss a lower bound on the number of crossing pairs of hyperedges in a complete geometric d-hypergraph. We also discuss the maximum crossing number of a complete geometric d-hypergraph for d<=4. We further discuss open questions in this regard and their connection to the polytope theory.
 
Jan 14 Vlad Makarov
28 Dimitrios Chiotis
Feb 11 Vsevolod Evtushevskiy
25 Boris Runov
Mar 11 Ilnur Baybulov
25 Alexey Semchenkov
Apr   8 Nikita Gaevoy
22 Sasha Kuznetsov
May   6 Julius Julius
20 Dimitrios Papathanasiou
Jun   3 Ignacio Vergara
17 Andrey Melnikov

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