Date
Friday November 19, 2021Location
Online via ZoomFriday, November 19th, 2021
Time: 12:00 p.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Deepanshu Prasad (Queen's University)
Title: Cross-Cut Theorem and Whitney's Theorem.
Abstract: I will prove the Cross-Cut Theorem and Whitney's Theorem and give some examples.
Date
Friday November 12, 2021Location
Online via ZoomFriday, November 12th, 2021
Time: 12:00 p.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Alexandre (Sasha) Zotine (Queen's University)
Title: Characteristic Polynomial of Arrangements.
Abstract: In this talk, we'll define the characteristic polynomial, which encodes several interesting invariants of an arrangement in one nice algebraic package. To compute characteristic polynomials, we'll introduce two tools: the Deletion/Restriction property, and Whitney's Theorem.
Date
Friday November 5, 2021Location
Online via ZoomFriday, November 5th, 2021
Time: 12:00 p.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Sonja Ruzic (Queen's University)
Title: Characteristic Polynomials and Projectivization.
Abstract: In this talk, I will continue last week’s discussion of the Möbius function and characteristic polynomial. I will also introduce the projectivization of a linear arrangement and give some examples.
Date
Friday October 29, 2021Location
Online via ZoomFriday, October 29th, 2021
Time: 12:00 p.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Deepanshu Prasad (Queen's University)
Title: Intersection Posets and Characteristic Polynomials.
Abstract: I will be talking about the Intersection Posets, Mobius Function of a Poset and the Characeristic Polynomial of an Arrangement. If time permits, then I will also discuss the Projectivization of a Linear Arrangement.
Date
Friday October 22, 2021Location
Online via ZoomFriday, October 22nd, 2021
Time: 12:00 p.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Alexandre (Sasha) Zotine (Queen's University)
Title: An Introduction to Hyperplane Arrangements.
Abstract: In this talk, I will give introduce hyperplane arrangements, and some basic defining properties associated with them. We will look at several examples, including the Braid arrangement, which is likely to reappear often.
Date
Monday February 7, 2022Location
Online via ZoomMonday, February 7th, 2022
Time: 11:00 a.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Deepanshu Prasad (Queen's University)
Title: Coxeter arrangements and Shi arrangements.
Abstract: We will look at the Coxeter arrangements, arising from root systems, and Shi arrangements. We will calculate their characteristic polynomial using the finite field method and talk about their "supersolvability" and "freeness".
Date
Monday January 31, 2022Location
Online via ZoomMonday, January 31st, 2022
Time: 11:00 a.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Alexandre (Sasha) Zotine (Queen's University)
Title: Graphical Arrangements cont.
Abstract: We will finish our discussion of graphical arrangements by covering orientations of graphs and relating them to the regions of their associated arrangements. Once this is finished, I will start to introduce some finite field methods for computing characteristic polynomials over the rationals.
Date
Monday January 24, 2022Location
Online via ZoomMonday, January 24th, 2022
Time: 11:00 a.m. Place: Online via Zoom (contact Deepanshu Prasad for Zoom link)
Speaker: Alexandre (Sasha) Zotine (Queen's University)
Title: Graphical Arrangements.
Abstract: Continuing our discussion of hyperplane arrangements, I will give a quick reminder of the talks that Ben gave on matroids, then proceed to introduce arrangements arising from graphs.
Date
Friday February 11, 2022Location
Online (via Zoom)
Friday, February 11th, 2022
Time: 2:30 p.m. Place: Online (via Zoom)
Speaker: Somnath Pradhan (Queen's University)
Title: Robustness of Stochastic Optimal Control for Controlled Diffusions with Incorrect Models
Abstract: In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model and the assumed model. A robustness problem in this context is to show that the error due to the mismatch between true model and assumed model decreases to zero as the assumed model approaches the true model. We study this problem when the state dynamics of the system are governed by controlled diffusion processes. In particular, we will discuss continuity and robustness properties of infinite-horizon $\alpha$-discounted/ergodic optimal control problems for a general class of controlled diffusion processes. Under a general set of assumptions and a convergence criterion on the models, we first establish that the optimal value of the approximate model converges to the optimal value of the true model. We then establish that the error due to mismatch that occurs by application of a control policy, designed for an incorrectly estimated model, to a true model decreases to zero as the incorrect model approaches the true model. We will see that, compared to related results in the discrete-time setup, the continuous-time theory will let us utilize the strong regularity properties of solutions to optimality (HJB) equations, via the theory of uniformly elliptic PDEs, to arrive at strong continuity and robustness properties. A corollary of our analysis is a continuity result on the optimal cost in the control policies under a natural topology which also leads to near-optimality of quantized stationary policies.
Somnath Pradhan is a Coleman postdoctoral fellow in the Department of Mathematics and Statistics at Queen's University. He was a postdoc fellow at the Indian Institute of Science Education and Research, Pune, India from 2019-2021. He obtained his Ph.D.~in Mathematics from Indian Institute of Science in 2019. His research interests include stochastic analysis, applied probability, and controlled Markov processes.
Date
Monday February 7, 2022Location
Online via ZoomMonday, February 7th, 2022
Time: 4:30 p.m. Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)
Speaker: Dixy Msapato (University of Leeds)
Title: Counting tau-exceptional sequences for Nakayama algebras.
Abstract: The notion of a tau-exceptional sequence was introduced by Buan and Marsh in 2018 as a generalisation of exceptional sequences over finite dimensional algebras. In this talk, I will introduce both this notion, and present counting results of tau-exceptional sequences over some classes of Nakayama algebras (and a general counting strategy). In some of these Nakayama algebra cases we will see obtain closed formulas counting other well-known combinatorial objects, and exceptional sequences over some path algebras of Dynkin quivers.
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