Dynamics, Geometry and Groups Seminar

Monday, November 13th, 2023

Time: 11:00 a.m.  Place: Jeffery Hall, Room 319

Speaker: Annika Fuernsinn (Queen's University)

Title: Towards Model Predictive Control

Abstract: In this talk, I provide some insights into my research for non-control mathematicians. We start with dynamical systems, but then enter into the control world and try to solve an infinite-horizon optimal control problem. As it turns out, this is quite a difficult problem and we can instead approximate the solution by considering the framework of Model Predictive Control (MPC). In the remaining talk we will discuss some shortcomings of MPC and try to provide resolutions. The idea is to introduce some flexibility into the standard MPC scheme, from which we deduce the novel flexible-step MPC scheme.

Curves Seminar

Thursday, November 9th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Sonja Ruzic

Title: More Examples and Laurent Polynomials

Abstract: Last week we noticed that each cluster variable can be expressed as a Laurent polynomial with integer coefficients in the elements of any extended cluster. This week we will see why that is the case, and we will look at some more examples of rank 2 cluster algebras.

Number Theory Seminar

Tuesday, November 7th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

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

Title: HIGHER CONVOLUTIONS OF RAMANUJAN SUMS

Abstract: We will discuss limit formulas for higher convolutions of Ramanujan sums and give applications to present a heuristic derivation of the Hardy-Littlewood conjectural formula for the number of k-tuples of primes. This is joint work with Shivani Goel.

Math & Stats Department Colloquium

Friday, November 3rd, 2023

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

Speaker: Jessica Lin (McGill University)

Title: Quantitative Homogenization for Nondivergence Form Equations

Abstract: In this talk, I will first give an introduction to stochastic homogenization for nondivergence form elliptic equations (from the PDE perspective) and quenched invariance principles for nonreversible diffusion processes (from the probability perspective). I will then present new quantitative homogenization results for the fundamental solution and the unique ergodic invariant measure. I will discuss the implications of these homogenization results, such as heat kernel bounds on the fundamental solution and quantitative ergodicity for the environmental process. This talk is based on joint work with Scott Armstrong (NYU) and Benjamin Fehrman (LSU).

Bio: Prof. Jessica Lin is an Associate Professor at McGill University and a CRC in Partial Differential Equations and Probability. Before McGill, she received her PhD from the University of Chicago and did a postdoc at the University of Wisconsin–Madison. Her research is broadly focused on the asymptotic behaviour of random physical systems, with an emphasis on stochastic homogenization, limit theorems, and effective phase transitions in various models subject to randomness.

Curves Seminar

Thursday, November 2nd, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Alexandre (Sasha) Zotine

Title: Examples of Cluster Algebras

Abstract: We'll look at several examples of cluster algebras in order to soak in the definition. We will also discuss some remarks about the definition.

Number Theory Seminar

Tuesday, October 31st, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Abhishek Bharadwaj (Queen's University)

Title: Algebraic Numbers with Integral Power Traces

Abstract: In this paper, the following result is proved : To determine if an algebraic number \alpha of degree n is an algebraic integer, it suffices to show that the trace of the powers \alpha^i is an integer for all positive i up to n + n log2n. We shall describe the key ingredients of the proof.

Dynamics, Geometry and Groups Seminar

Monday, October 30th, 2023

Time: 11:00 a.m.  Place: Jeffery Hall, Room 319

Speaker: Federico Salmoiraghi (Queen's University)

Title: Contact structures, open books and Heegaard Floer homology

Abstract: Hegaard Floer homology is a package of powerful algebraic invariant for 3-manifolds. After giving the necessary background we will see some application of Heegaard Floer theory to 3-dimensional contact geometry.

Curves Seminar

Thursday, October 26th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Luke Steverango

Title: Seed Patterns and Cluster Algebras

Abstract: In this talk, we will define one last piece of mathematical machinery that is central to defining a cluster algebra, a seed pattern. A seed pattern is a combinatorial way to keep track of mutations between cluster variables. We will then give the definition of a cluster algebra, explore some of the consequences of the definition, and explore some examples.

Math & Stats Department Colloquium

Friday, October 27th, 2023

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

Speaker: Carl Mautner (University of California - Riverside)

Title: Symmetric groups, Schur algebras and Hilbert schemes

Abstract: In his 1901 thesis, Issai Schur discovered a connection between the representation theory of the symmetric group and general linear group. One way to understand this connection is through a finite dimensional algebra called the Schur algebra. I will outline this picture and then describe a new algebra, defined in joint work with Tom Braden, and some of its nice properties. Finally, I will explain how we came to discover this algebra by studying the geometry of the Hilbert scheme of points in the plane.

Bio: Prof. Carl Mautner is an associate professor at UC Riverside. He received his PhD from the University of Texas, Austin in 2010. He was then a postdoctoral fellow at Harvard and the Max Planck Institut in Bonn, before joining the faculty at UC Riverside in 2015. He also held a visiting position at Dartmouth. Prof. Mautner’s work is in geometric representation theory, a field at the intersection of algebra, topology, algebraic geometry and combinatorics. When not doing math, Prof. Mautner sometimes sparks, knowingly or not, wildflower superblooms in his backyard.

Number Theory Seminar

Tuesday, October 24th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Shivani Goel (IIIT-Delhi)

Title: On the Hardy Littlewood 3-tuple prime conjecture and convolutions of Ramanujan sums.

Abstract: The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of Ramanujan sums. Building upon their work, we explore triple convolution Ramanujan sums and use this approach to provide a heuristic derivation of the Hardy-Littlewood conjecture concerning prime 3-tuples. Furthermore, we estimate the triple convolution of the Jordan totient function using Ramanujan sums.