Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Geometry & Representation - John Michael Machacek (York University)

Monday, October 7th, 2019

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

Speaker: John Michael Machacek (York University)

Title: Mutation combinatorics and upper cluster algebras.

Abstract:  Any cluster algebra is contained in an intersection of Laurent polynomial rings known as its upper cluster algebra. There are known cases where this containment is equality as well as cases of strict containment. We will discuss combinatorial approaches to determining if this containment is strict or not. Notions used will include reddening sequences and locally acyclic cluster algebras.

Department Colloquium - Diane Maclagan (Warwick)

Diane Maclagan (Warwick)

Friday, October 4th, 2019

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

Speaker: Diane Maclagan (Warwick)

Title: Geometry of the moduli space of genus zero curves.

Abstract: The moduli space $\overline{M}_{0,n}$ of stable genus zero curves with $n$ marked points is a beautiful space that has been intensively studied by algebraic geometers and topologists for over half a century. It arises from a simple geometric question ("How can we arrange $n$ points on a sphere?"), but is the first nontrivial case of several interesting families of varieties (higher genus curves, stable maps, ...) and phenomena. Despite the long history there are still many mysteries about this variety. I will introduce this moduli space, and discuss some combinatorial approaches to understanding it.

Diane Maclagan (Warwick) is a Professor of Mathematics at the University of Warwick. She received her PhD from UC Berkeley, and moved to Warwick from Rutgers, following postdocs at IAS and Stanford. Her research is in Combinatorial Algebraic Geometry, with a particular focus on Tropical Geometry.

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