Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Jeremy Quastel (University of Toronto)

Jeremy Quastel (University of Toronto)

Friday, October 18th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Jeremy Quastel (University of Toronto)

Title: The KPZ fixed point.

Abstract: The one dimensional KPZ universality class contains random growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g.~the eponymous Kardar--Parisi--Zhang equation). It is characterized by unusual scale of fluctuations, some of which appeared earlier in random matrix theory, and which depend on the initial data, the explanation being that on large scales everything approaches a special scaling invariant Markov process, the KPZ fixed point, which turns out to be a new type of integrable system, leading to unexpected connections between probability and dispersive partial differential equations.

Prof. Jeremy Quastel specializes in probability theory, stochastic processes and partial differential equations. He obtained is Ph.D.~from the Courant Institute at NYU. He was a postdoctoral fellow at the MSRI in Berkeley, then was a faculty at UC-Davis until he returned to Canada in 1998, where he is now a professor at the University of Toronto and the current chair of the Mathematics department.

Among his accolades, Prof. Quastel received a Sloan Fellowship in 1996, was an invited speaker at the ICM in 2010, gave the Current Developments in Mathematics 2011 and St. Flour 2012 lectures, and was a plenary speaker at the International Congress of Mathematical Physics in Aalborg 2012. He is a fellow of the Royal Society of Canada.

Dynamics, Geometry, & Groups - Heejoung Kim (UIUC)

Thursday, October 17th, 2019

Time: 3:30 p.m Place: Jeffery Hall 319

Speaker: Heejoung Kim (University of Illinois, Urbana-Champaign)

Title: Algorithms detecting stability and Morseness for finitely generated groups.

Abstract: For a word-hyperbolic group G, the notion of quasiconvexity is independent on the choice of a generating set and a quasiconvex subgroup of G is quasi-isometrically embedded in G. Kapovich provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise. However, beyond word-hyperbolic groups, the notion of quasiconveixty is not as useful. For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, a ``stable'' subgroup and a ``Morse'' subgroup. In this talk, we will discuss various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups.

Number Theory Seminar - Brad Rodgers (Queen's University)

Thursday, October 17th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Brad Rodgers (Queen's University)

Title: Moments and pseudomoments of the Riemann zeta-function, pt. 2.

Abstract: In a previous talk we discussed moments of the Riemann zeta function and "pseudomoments", in which the zeta-function is replaced by a finite Dirichlet polynomial. In this second talk we will further discuss random multiplicative functions and a variant of conjecture of Helson, proved with averaging weights by Bondarenko, Heap, and Seip. I hope to reintroduce the fundamental notions, so that this talk can be followed by audience members who missed the previous talk.

CYMS Seminar - Fenglong You (University of Alberta)

Thursday, October 17th, 2019

Time: 2:30 p.m Place: Jeffery Hall 319

Speaker: Fenglong You (University of Alberta)

Title: Relative Gromov--Witten theory and mirror symmetry

Abstract: Gromov--Witten theory is considered as the first modern approach in enumerative geometry. Absolute Gromov--Witten invariants provide virtual counts of curves in smooth projective varieties/orbifolds. It is known to have many nice structural properties, such as quantum cohomology, WDVV equation, Givental's formalism, mirror theorem, CohFT etc.. Relative Gromov--Witten invariants study the virtual counts of curves in varieties with tangency conditions along a divisor. In this talk, I will give an overview of some recent developments on parallel structures of relative Gromov--Witten theory. If time permits, I will also talk about some applications such as SYZ mirror symmetry and Doran--Harder--Thompson conjecture.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, October 16th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Classical results on canonical embeddings II.

Abstract: We will discuss the Hilbert polynomial and Hilbert function of canonically embedded curves, classical theorems of Noether, Castelnuovo, Enriques-Babbage, and Petri, and work out the minimal free resolutions of the homogenous coordinate rings of canonically embedded curves in small genus.

Department Colloquium - Eugene A. Feinberg (Stony Brook University)

Eugene A. Feinberg (Stony Brook University)

Friday, October 11th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Eugene A. Feinberg (Stony Brook University)

Title: Fatou's Lemmas for Varying Probabilities and their Applications to Sequential Decision Making.

Abstract: The classic Fatou lemma states that the lower limit of expectations is greater or equal than the expectation of the lower limit for a sequence of nonnegative random variables. This talk describes several generalizations of this fact including generalizations to converging sequences of probability measures. The three types of convergence of probability measures are considered in this talk: weak convergence, setwise convergence, and convergence in total variation. The talk also describes the Uniform Fatou Lemma (UFL) for sequences of probabilities converging in total variation. The UFL states the necessary and sufficient conditions for the validity of the stronger inequality than the inequality in Fatou's lemma. We shall also discuss applications of these results to sequential optimization problems with completely and partially observable state spaces. In particular, the UFL is useful for proving weak continuity of transition probabilities for posterior state distributions of stochastic sequences with incomplete state observations known under the name of Partially Observable Markov Decision Processes. These transition probabilities are implicitly defined by Bayes' formula, and general method for proving their continuity properties have not been available for long time. This talk is based on joint papers with Pavlo Kasyanov, Yan Liang, Michael Zgurovsky, and Nina Zadoianchuk.

Prof. Eugene Feinberg is currently a Distinguished Professor in the Department of Applied Mathematics and Statistics at Stony Brook University. Before coming to Stony Brook, he help positions at Moscow State University of Railway Transportation and Yale. He obtained his Ph.D. from Vilnius University, Lithuania.

Prof. Feinberg is a Fellow of INFORMS and has received several awards including the 2012 IEEE Charles Hirsh Award, the 2012 IBM Faculty Award, and the 2000 Industrial Associates Award from Northrop Grumman.

Number Theory Seminar - M. Ram Murty (Queen's University)

Thursday, October 10th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: M. Ram Murty (Queen's University)

Title: THE PALEY GRAPH CONJECTURE AND DIOPHANTINE TUPLES.

Abstract: Let $n$ be a fixed natural number. An $m$-tuple $(a(1), ..., a(m))$ is said to be a Diophantine $m$-tuple with property $D(n)$ if $a(i)a(j)+n$ is a perfect square for $i, j$ distinct and less than or equal to $m$. We will show that the Paley graph conjecture in graph theory implies that the number of such tuples is $O((log n)^c)$ for any $c>0$. This is joint work with Ahmet Guloglu.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, October 9th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Classical results on canonical embeddings.

Abstract: We will discuss the canonical map in the case of hyperelliptic curves, the geometric interpretation of the Riemann-Roch theorem via the canonical map, the Hilbert polynomial and Hilbert function of canonically embedded curves, and start looking at examples of resolutions of canonical embeddings in small genus.

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