Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Control Theory - Christoph Kawan (University of Passau)

Thursday, September 27th, 2018

Time: 9:00-10:30 a.m Place: Jeffery Hall 319

Speaker: Christoph Kawan (University of Passau)

Title: Robust estimation under information constraints for deterministic non-linear systems

Abstract: A fundamental problem in information-based control is to estimate the state of a dynamical system using information sent through a rate-limited channel. In this talk, we explain the concept of restoration entropy, introduced by Matveev and Pogromsky, which characterizes the smallest channel capacity above which a robust coding and estimation policy with arbitrarily small estimation error can be implemented. In particular, we provide a characterization of restoration entropy that involves no asymptotic quantities and leads to nearly optimal policies.

CYMS Seminar - Noriko Yui (Queen's University)

Thursday, September 27th, 2018

Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422

Speaker: Noriko Yui (Queen's University)

Title: Four-dimensional Galois representations arising from certain Calabi--Yau threefolds

Abstract: We consider the (irreducible) four-dimensional Galois representations arising from certain Calabi--Yau threefolds over ${\bf{Q}}$ with all the Hodge numbers of the third cohomology groups equal to $1$. There are many examples of (families) of such Calabi--Yau threefolds. The modularity/automorphy of such Calabi--Yau threefolds will be the main topic of discussion. There are two venues to be considered. In one venue, we ought to count the number of rational points over finite fields of these Calabi--Yau threefolds to concoct their L-series. In the other venue, we ought to construct some modular varieties, in this case, conjecturally, Siegel modular forms of weight $3$ and genus $2$ on some paramodular subgroups of $Sp(4,{\bf{Z}})$, and then compute their L-series. Such modular forms may be constructed using Borcherds forms. The ultimate aim is to establish a Langlands correspondence between the two L-series, thereby establishing the modularity/automorphy of such Calabi--Yau threefolds.

This is a joint work with Yifan Yang (National Taiwan University).

Number Theory - Neha Prabhu (Queen's University)

Tuesday, September 25th, 2018

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

Speaker: Neha Prabhu (Queen's University)

Title: The error term in the Sato-Tate theorem of Birch.

Abstract: In 1968, Birch proved a vertical analogue of the Sato-Tate conjecture for elliptic curves showing the asymptotic behaviour of $a_E(p)$, a quantity associated to an elliptic curve $E$ mod p. An error term for this result was obtained by Banks and Shparlinski in 2009 using the results of Katz and Neiderreiter. In this talk, we shall see that this error term can also be obtained in an elementary fashion using ideas in Birch's paper. This is joint work with Ram Murty.

Geometry & Representation - Emine Yildrim (Queen's University)

Monday, September 24th, 2018

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

Speaker: Emine Yildrim (Queen's University)

Title: The bounded derived category for cominuscule posets

Abstract:  Cominuscule posets come from root posets and have connections to Lie theory and Schubert calculus. We are interested in whether the bounded derived category of the incidence algebra of a cominuscule poset is fractionally Calabi-Yau. In other words, we ask if some non-zero power of the Serre functor is a shift functor. We answer this question on the level of the Grothendieck groups. On the Grothendieck group this functor becomes an endomorphism called the Coxeter transformation. We show that Coxeter transformation has finite order for two of the three infinite families of cominuscule posets, and for the exceptional cases. Our motivation comes from a conjecture by Chapoton which states that the bounded derived category of incidence algebra of root posets is fractionally Calabi-Yau. Our result can be thought of as a parabolic analogue of Chapoton's conjecture.

Department Colloquium - Boris Levit (Queen's University)

Boris Levit, Queen's University

Friday, September 21st, 2018

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

Speaker: Boris Levit (Queen's University)

Title: Optimal Cardinal Interpolation in Approximation Theory, Nonparametric Regression, and Optimal Design

Abstract: For the Hardy classes of functions analytic in the strip around real axis of a size $2\beta$, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery. It will be shown that this method, based on the Jacobi elliptic functions, is also optimal according to the criteria of Nonparametric Regression and Optimal Design. In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from $0$. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant's bias and variance mutually cancel each other. In the limiting case $\beta \rightarrow \infty $, the optimal interpolant converges to the well known Nyquist-Shannon cardinal sampling series.

Probability Seminar - Jamie Mingo (Queen's University)

Thursday, September 20th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Jamie Mingo (Queen's University)

Title: I will begin by reviewing the basic facts of scalar free independence

Abstract:  This fall the seminar will be a learning seminar with lectures by (willing) participants. The theme will be operator valued freeness. This is the non-commutative version of conditional independence, now we have independence over a subalgebra. In many cases the subalgebras are n x n matrices so this is quite a general situation.

I will begin by reviewing the basic facts of scalar free independence. The seminar will follow a recent book by D. Kaliuzhnyi-Verbovetskyi and V. Vinnikov and some lecture notes of D. Jekel.

Free Probability and Random Matrices Seminar Webpage:

CYMS Seminar - Richard Gottesman (Queen's University)

Thursday, September 20th, 2018

Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422

Speaker: Richard Gottesman (Queen's University)

Title: Vector-Valued Modular Forms on $\Gamma_{0}(2)$C

Abstract: The collection of vector-valued modular forms form a graded module over the graded ring of modular forms. I will explain how understanding the structure of this module allows one to show that the component functions of vector-valued modular forms satisfy an ordinary differential equation whose coefficients are modular forms. In certain cases, we can use a Hauptmodul to transform such a differential equation into a Fuchsian differential equation on the projective line minus three points. We then are able to use the Gaussian hypergeometric series to explicitly solve this differential equation.
Finally, we make use of these ideas together with some algebraic number theory to study the prime numbers that divide the denominators of the Fourier coefficients of the component functions of vector-valued modular forms.

Number Theory - Zhen Zhao (Queen's University)

Tuesday, September 18th, 2018

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

Speaker: Zhen Zhao (Queen's University) 

Title: Asymptotics of the dimensions of irreducible representations of the symmetric group

Abstract: We will discuss the results of the 1985 paper of S. V. Kerov and A. M. Vershik giving the asymptotic rates growth for the dimensions of the largest and 'typical' dimensions of the irreducible representations of the symmetric group of order n.

Geometry & Representation - Tianyuan Xu (Queen's University)

Monday, September 17th, 2018

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

Speaker: Tianyuan Xu (Queen's University)

Title: Broken lines and the topological ordering of the alternating quiver of type A

Abstract:  The Positivity Conjecture in cluster algebra theory states that the coefficients of the Laurent expansion of any cluster variable in a cluster algebra are always positive integers. In 2014, Gross, Hacking, Keel and Kontsevich constructed a so-called Theta function basis to prove the conjecture for all cluster algebras of geometric type. A key ingredient in the construction of the Theta functions is the broken line model. In this talk, we will discuss the broken lines associated to the alternating quiver of type A, with an emphasis on relating its combinatorial properties to the topological ordering of the quiver, the partial order obtained by taking the transitive and reflexive losure of the relation “v<w if v->w is an edge” on the vertices of the quiver.

The talk is based work in progress with Ba Nguyen, David Wehlau and Imed Zaguia.

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