Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Geometry & Representation - Yin Chen (NE Normal University, China)

Monday, November 12th, 2018

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

Speaker: Yin Chen (Northeast Normal University, China)

Title: On vector invariant fields for finite classical groups

Abstract:  In the recent work (https://doi.org/10.1016/j.jpaa.2018.07.015) with David Wehlau, we found a minimal polynomial generating set for the vector and covector invariant field of the general linear group over finite fields. Our method relied on some relations between the generators for the invariant ring of one vector and one covector. The remaining case (without covectors) is more complicated. In this talk, I will present an approach to find polynomial generating sets for the vector invariant fields of the most of finite classical groups. This is a joint work with Zhongming Tang.

Department Colloquium - Dennis K. J. Lin (Penn State University)

Dennis K. J. Lin (Penn State University)

Friday, November 9th, 2018

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

Speaker: Dennis K. J. Lin (Penn State University)

Title: Ghost Data.

Abstract: As natural as the real data, ghost data is everywhere -- it is just data that you cannot see. We need to learn how to handle it, how to model with it, and how to put it to work. Some examples of ghost data are (see, Sall, 2017):
a) Virtual data -- it isn't there until you look at it;
b) Missing data -- there is a slot to hold a value, but the slot is empty;
c) Pretend data -- data that is made up;
d) Highly Sparse Data -- whose absence implies a near zero, and
e) Simulation data -- data to answer ``what if.''
For example, absence of evidence/data is not evidence of absence. In fact, it can be evidence of something. More Ghost Data can be extended to other existing areas: Hidden Markov Chain, Two-stage Least Square Estimate, Optimization via Simulation, Partition Model, Topological Data, just to name a few. Three movies will be discussed in this talk: (1) ``The Sixth Sense'' (Bruce Willis) -- I can see things that you cannot see; (2) ``Sherlock Holmes'' (Robert Downey) -- absence of expected facts; and (3) ``Edge of Tomorrow'' (Tom Cruise) -- how to speed up your learning (AlphaGo-Zero will also be discussed). It will be helpful, if you watch these movies before coming to my talk. This is an early stage of my research in this area--any feedback from you is deeply appreciated. Much of the basic idea is highly influenced via Mr. John Sall (JMP-SAS).

Dennis K. J. Lin (Penn State University): He is a university distinguished professor of supply chain and statistics at Penn State University. His research interests are quality assurance, industrial statistics, data mining, and response surface. He has published more than 200 SCI/SSCI papers in a wide variety of journals. He currently serves or has served as associate editor for more than 10 professional journals and was co-editor for Applied Stochastic Models for Business and Industry. Dr. Lin is an elected fellow of ASA, IMS and ASQ, an elected member of ISI, a lifetime member of ICSA, and a fellow of RSS. He is an honorary chair professor for various universities, including a Chang-Jiang Scholar at Renmin University of China, Fudan University, and National Chengchi University (Taiwan). His recent awards including, the Youden Address (ASQ, 2010), the Shewell Award (ASQ, 2010), the Don Owen Award (ASA, 2011), the Loutit Address (SSC, 2011), the Hunter Award (ASQ, 2014), and the Shewhart Medal (ASQ, 2015). Last year, he was awarded the SPES Award at the 2016 Joint Statistical Meeting.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 6th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Local description of the Hilbert scheme when $n=2$, II.

Abstract: We will finish the discussion of local descriptions of the quotient by a finite group, and use them to give local pictures of $X^{[n]}$, $\operatorname{Sym}^n(X)$, the universal family over $X^{[n]}$, and the maps between them when $X$ is a smooth surface and $n=2$.

Number Theory - Brad Rodgers (Queen's University)

Tuesday, November 6th, 2018

Time: 10:00-11:00 a.m.  Place: Jeffery Hall 422

Speaker: Brad Rodgers (Queen's University)

Title: Integers in short intervals representable as sums of two squares.

Abstract: Consider the set S of integers that can be represented as a sum of two squares. How are the elements of S distributed? In particular, how many elements fall into a random "short interval". (The definition of short interval will be given in the talk.) For very short intervals elements of S seem to be laid down at random, but I will discuss evidence that this ceases to be the case for longer short intervals. In particular, I will discuss a function field analogue of this problem and a connection to z-measures, an object first investigated in the context of asymptotic representation theory. This is joint work with O. Gorodetsky.

Geometry & Representation - Steven Spallone (Indian Institute)

Monday, November 5th, 2018

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

Speaker: Steven Spallone (Indian Institute of Science Education and Research)

Title: Spinoriality of Orthogonal Representations of Reductive Groups

Abstract:  Let G be a connected semisimple complex Lie group and $\pi$ an orthogonal representation of G. We give a simple criterion for whether $\pi$ lifts to the spin group Spin(V), in terms of its highest weights. This is joint work with Rohit Joshi.

Department Colloquium - Thomas Koberda (University of Virginia)

Thomas Koberda (University of Virginia)

Friday, November 2nd, 2018

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

Speaker: Thomas Koberda (University of Virginia)

Title: Algebra versus regularity for group actions on one-manifolds.

Abstract: I will survey some results concerning the algebraic structure of finitely generated groups which admit faithful actions on compact one-manifolds. I will concentrate on continuous, $C^1$, and $C^2$ actions, and on the various algebraic restrictions imposed by regularity requirements. Of particular interest will be nilpotent groups, right-angled Artin groups, mapping class groups of surface, and Thompson's groups F and T. Time permitting, I will indicate some recent progress.

After obtaining his undergraduate at the University of Chicago, Thomas Koberda got his Ph.D.~from Harvard in 2012, then went to Yale as an NSF and Gibbs assistant professor before joining the University of Virginia in 2015. Thomas achievements have been recognized by a Sloan Research Fellowship and the Kamil Duszenko Prize of 2017.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, October 30th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Local description of the Hilbert scheme when n=2

Abstract: Given a smooth surface $X$, we have the Hilbert scheme of points $X^{[n]}$, the associated Hilbert-Chow morphism to $\operatorname{Sym}^n(X)$, and the universal family over $X^{[n]}$. We will study what these look like when $n=2$.

Number Theory - Neha Prabhu (Queen's University)

Tuesday, October 30th, 2018

Time: 10:00-11:00 a.m.  Place: Jeffery Hall 422

Speaker: Neha Prabhu (Queen's University)

Title: Central limit theorems in number theory.

Abstract: In this talk, I will report on joint work in progress with Ram Murty, where we obtain central limit theorems for sums of quadratic characters, and eigenvalues of Hecke operators acting on spaces of holomorphic cusp forms.

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