Seminars and Colloquia by Series

Wednesday, August 29, 2018 - 12:55 , Location: Skiles 006 , Konstantin Tikhomirov , GeorgiaTech , Organizer: Konstantin Tikhomirov
We show that there is a symmetric n-dimensional convex set whose Banach--Mazur distance to the cube is bounded below by n^{5/9}/polylog(n). This improves previously know estimate due to S.Szarek, and confirms a conjecture of A.Naor. The proof is based on probabilistic arguments.
Wednesday, August 29, 2018 - 01:55 , Location: Skiles 005 , Michael Lacey , Georgia Tech , Organizer: Michael Lacey
Spherical averages, in the continuous and discrete setting, are a canonical example of averages over lower dimensional varieties. We demonstrate here a new approach to proving the sparse bounds for these opertators.  This approach is a modification of an old technique of Bourgain. 
Monday, August 27, 2018 - 14:30 , Location: Boyd , TBA , TBA , Organizer: Caitlin Leverson
Wednesday, August 22, 2018 - 14:00 , Location: Skiles 005 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay

This theorem is one of earliest instance of the h-principle, and there will be a series of talks on it this semester.

The Whitney-Graustein theorem classifies immersions of the circle in the plane by their turning number. In this talk, I will describe a proof of this theorem, as well as a related result due to Hopf.
Series: PDE Seminar
Tuesday, August 21, 2018 - 15:00 , Location: Skiles 006 , Professor Veli Shakhmurov , Okan University , veli.sahmurov@okan.edu.tr , Organizer: Ronghua Pan
Monday, August 20, 2018 - 15:05 , Location: Skiles 005 , Esther Ezra , Georgia Tech , Organizer: Prasad Tetali
A recent extension by Guth (2015) of the basic polynomial partitioning technique of Guth and Katz (2015) shows the existence of a partitioning polynomial for a given set of k-dimensional varieties in R^d, such that its zero set subdivides space into open cells, each meeting only a small fraction of the given varieties.  For k > 0, it is unknown how to obtain an explicit representation of such a partitioning polynomial and how to construct it efficiently.  This, in particular, applies to the setting of n algebraic curves, or, in fact, just lines, in 3-space.  In this work we present an efficient algorithmic construction for this setting almost matching the bounds of Guth (2015); For any D > 0, we efficiently construct a decomposition of space into O(D^3\log^3{D}) open cells, each of which meets at most O(n/D^2) curves from the input.  The construction time is O(n^2), where the constant of proportionality depends on the maximum degree of the polynomials defining the input curves.  For the case of lines in 3-space we present an improved implementation using a range search machinery. As a main application, we revisit the problem of eliminating depth cycles among non-vertical pairwise disjoint triangles in 3-space, recently been studied by Aronov et al.  Joint work with Boris Aronov and Josh Zahl.
Series: Other Talks
Tuesday, August 14, 2018 - 14:00 , Location: Skiles 154 , Justin Lanier , Georgia Tech , jlanier8@gatech.edu , Organizer: Justin Lanier
Take a branched covering map of the sphere over itself so that the forward orbit of each critical point is finite. Such maps are called Thurston maps. Examples include polynomials with well-chosen coefficients acting on the complex plane, as well as twists of these by mapping classes. Two basic problems are classifying Thurston maps up to equivalence and finding the equivalence class of a Thurston map that has been twisted. We will discuss ongoing joint work with Belk, Margalit, and Winarski that provides a new, combinatorial approach to the twisted polynomial problem. We will also propose several new research directions regarding Thurston maps. This is an oral comprehensive exam. All are welcome to attend.
Friday, July 20, 2018 - 13:00 , Location: Skiles 006 , Kashyap Rajeevsarathy , IISER Bhopal , Organizer: Dan Margalit
Let Mod(Sg) denote the mapping class group of the closed orientable surface Sg of genus g ≥ 2. Given a finite subgroup H < Mod(Sg), let Fix(H) denote the set of fixed points induced by the action of H on the Teichmuller space Teich(Sg). In this talk, we give an explicit description of Fix(H), when H is cyclic, thereby providing a complete solution to the Modular Nielsen Realization Problem for this case. Among other applications of these realizations, we derive an intriguing correlation between finite order maps and the filling systems of surfaces. Finally, we will briefly discuss some examples of realizations of two-generator finite abelian actions.
Monday, July 2, 2018 - 01:55 , Location: Skiles 005 , Isabelle Kemajou-Brown , Morgan State University , elisabeth.brown@morgan.edu , Organizer: Luca Dieci
We assume the stock is modeled by a Markov regime-switching diffusion process and that, the benchmark depends on the economic factor. Then, we solve a risk-sensitive benchmarked asset management problem of a firm. Our method consists of finding the portfolio strategy that minimizes the risk sensitivity of an investor in such environment, using the general maximum principle.After the above presentation, the speaker will discuss some of her ongoing research.
Friday, June 29, 2018 - 13:00 , Location: Skiles 005 , Tongzhou Chen , School of Mathematics , tchen308@gatech.edu , Organizer: Tongzhou Chen
We model and analyze the dynamics of religious group membership and size. A groups is distinguished by its strictness, which determines how much time group members are expected to spend contributing to the group. Individuals differ in their rate of return for time spent outside of their religious group. We construct a utility function that individ- uals attempt to maximize, then find a Nash Equilibrium for religious group participation with a heterogeneous population. We then model dynamics of group size by including birth, death, and switching of individuals between groups. Group switching depends on the strictness preferences of individuals and their probability of encountering members of other groups. We show that in the case of only two groups one with finite strictness and the other with zero there is a clear parameter combination that determines whether the non-zero strictness group can survive over time, which is more difficult at higher strictness levels. At the same time, we show that a higher than average birthrate can allow even the highest strictness groups to survive. We also study the dynamics of several groups, gaining insight into strategic choices of strictness values and displaying the rich behavior of the model. We then move to the simultaneous-move two-group game where groups can set up their strictnesses strategically to optimize the goals of the group. Affiliations are assumed to have three types and each type of group has its own group utility function. Analysis on the utility functions and Nash equilibria presents different behaviors of various types of groups. Finally, we numerically simulated the process of new groups entering the reli- gious marketplace which can be viewed as a sequence of Stackelberg games. Simulation results show how the different types of religious groups distinguish themselves with regard to strictness.

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