## Seminars and Colloquia by Series

Friday, November 23, 2018 - 15:00 , Location: None , None , None , Organizer: Lutz Warnke
Friday, November 23, 2018 - 13:05 , Location: None , None , None , Organizer: He Guo
Monday, November 19, 2018 - 14:00 , Location: Skiles 006 , Livio Liechti , Paris-Jussieu , Organizer: Balazs Strenner
Mapping classes are the natural topological symmetries of surfaces. Their study is often restricted to the orientation-preserving ones, which form a normal subgroup of index two in the group of all mapping classes. In this talk, we discuss orientation-reversing mapping classes. In particular, we show that Lehmer's question from 1933 on Mahler measures of integer polynomials can be reformulated purely in terms of a comparison between orientation-preserving and orientation-reversing mapping classes.&nbsp;
Friday, November 16, 2018 - 15:05 , Location: Skiles 156 , Sergio Mayorga , Georgia Tech , Organizer: Jiaqi Yang
In this talk I will begin by discussing the main ideas of mean-field games and then I will introduce one specific model, driven by a smooth hamiltonian with a regularizing potential and no stochastic noise. I will explain what type of solutions can be obtained, and the connection with a notion of Nash equilibrium for a game played by a continuum of players.
Friday, November 16, 2018 - 15:00 , Location: Skiles 005 , , Georgia Tech , Organizer: Lutz Warnke
Let P be a system of unique shortest paths through a graph with real edge weights (i.e. a finite metric). An obvious fact is that P is "consistent," meaning that no two of these paths can intersect each other, split apart, and then intersect again later. But is that all? Can any consistent path system be realized as unique shortest paths in some graph? Or are there more forbidden combinatorial intersection patterns out there to be found? In this talk, we will characterize exactly which path systems can or can't be realized as unique shortest paths in some graph by giving a complete list of new forbidden intersection patterns along these lines. Our characterization theorem is based on a new connection between graph metrics and certain boundary operators used in some recent graph homology theories. This connection also leads to a principled topological understanding of some of the popular algebraic tricks currently used in the literature on shortest paths. We will also discuss some applications in theoretical computer science.
Friday, November 16, 2018 - 14:00 , Location: Skiles 006 , Stavros Garoufalidis , Georgia Tech and MPI , Organizer: John Etnyre
I will explain some connections between the counting of&nbsp;incompressible surfaces in hyperbolic 3-manifolds with boundary and the&nbsp;3Dindex of Dimofte-Gaiotto-Gukov. Joint work with N. Dunfield, C. Hodgson&nbsp;and H. Rubinstein, and, as usual, with lots of examples and patterns.
Friday, November 16, 2018 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Friday, November 16, 2018 - 14:00 , Location: Skiles 005 , , Florida State University , Organizer: Yoav Len
Let K be a non-trivially valued non-Archimedean field, R its valuation subring. A formal Gubler model is a formal R-scheme that comes from a polyhedral decomposition of a tropical variety. In this talk, I will present joint work with Sam Payne in which we show that any formal model of any compact analytic domain V inside a (not necessarily projective) K-variety X can be dominated by a formal Gubler model that extends to a model of X. This result plays a central role in our work on "structure sheaves" on tropicalizations and our work on adic tropicalization. If time permits I will explain some of this work.
Friday, November 16, 2018 - 13:05 , Location: Skiles 005 , , Math, University of Michigan , , Organizer: He Guo
Consider&nbsp; a&nbsp; linear&nbsp; combination&nbsp; of&nbsp; independent&nbsp; identically&nbsp; distributed&nbsp; random variables $X_1, . . . , X_n$ with fixed weights $a_1, . . . a_n$.&nbsp; If the random variablesare continuous, the sum is almost surely non-zero.&nbsp; However, for discrete random variables an exact cancelation may occur with a positive probability.&nbsp; Thisprobability depends on the arithmetic nature of the sequence $a_1, . . . a_n$.&nbsp; We will discuss how to measure the relevant arithmetic properties and how to evaluate the probability of the exact and approximate cancelation.
Friday, November 16, 2018 - 11:00 , Location: Skiles 006 , , University of Michigan , , Organizer: Galyna Livshyts