Date
Monday February 27, 2023Location
Jeffery Hall, Room 222Monday, February 27th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 222
Speaker: Colin Ingalls (Carleton University)
Title: Groupoids associated with non-commutative surfaces.
Abstract:
Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html
Date
Friday February 17, 2023Location
Jeffery Hall, Room 234Friday, February 17th, 2023
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Alejandra Quintos (University of Wisconsin–Madison)
Title: Dependent Stopping Times and an Application to Credit Risk Theory
Abstract: Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.
In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We show the impact of increasing the number of G-SIBs and that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.
We end the talk with some related and outgoing work that uses phase-type distributions.
This talk is based on joint work with Philip Protter, Robert Jarrow, Jianxi Su, and Yisub Kye.
Alejandra is an Assistant Professor and a Nellie McKay Fellow in the Department of Statistics at the University of Wisconsin-Madison. She completed her Ph.D. in Statistics at Columbia University where she held a Fulbright grant and received the Howard Levene Outstanding Teaching Award. Before graduate school, Alejandra had a merit scholarship to major in Actuarial Sciences at Universidad de las Américas Puebla from where she graduated Summa Cum Laude and was the Valedictorian of her class. Her research interests include problems in probability, stochastic processes, and statistics motivated by their applications, particularly in mathematical finance and more specifically in credit risk theory.
Date
Wednesday February 15, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, February 15th, 2023
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 & Zoom
Speaker: Deepanshu Prasad
Title: Projective Toric Varieties
Abstract: We'll finish our discussion of lattice polytopes by introducing the very ample property, then see how this allows us to construct projective toric varieties. We will then translate this construction into a more general framework via normal fans and discuss consequences.
Date
Monday February 13, 2023Location
Jeffery Hall, Room 319Monday, February 13th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Grayson Plumpton (Queen's University)
Title: An idelic approach to probability laws related to the Riemann zeta function
Abstract: In a 1999 paper by Biane, Pitman, and Yor, they construct a random variable whose expectation is related to Riemann's xi function. Using this, they give a probabilistic interpretation of the first two Li coefficients appearing in Li's criterion for the Riemann hypothesis. They take a classical approach, making use of Jacobi's theta function, which is at times messy and not easily generalizable to other Dedekind zeta functions. In this talk I discuss how one might reapproach this result by considering random variables on the idele group of a number field.
Date
Wednesday February 8, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, February 8th, 2023
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 & Zoom
Speaker: Deepanshu Prasad
Title: Lattice Polytopes and Normal Polytopes
Abstract: We will study lattice polytopes and normal polytopes, which will be useful in defining toric variety of poyltopes, and look at some examples
Date
Thursday February 9, 2023Location
Jeffery Hall, Room 118Thursday, February 9th, 2023
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: Francesco Cellarosi (Queen's University)
Title: A converse to the intermediate value theorem?
Abstract: Continuous functions satisfy the intermediate value property: on an interval $[a,b]$ they attain every value between $f(a)$ and $f(b)$. Is the converse true? That is, does the intermediate value property imply continuity? We will see that the answer is no, and discuss some extreme counterexamples of everywhere discontinuous functions with the intermediate value property.
Date
Monday February 13, 2023Location
TBAMonday, February 13th, 2023
Time: 4:30 p.m. Place: TBA
Speaker: David Wehlau (RMC & Queen's University)
Title: Determining whether the invariants of a modular permutation representation are Cohen-Macaulay
Abstract:
Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html
Date
Wednesday March 29, 2023Location
Jeffery Hall, Room 319Wednesday, March 29th, 2023
Time: 12:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Ben Landon (U of Toronto)
Title: Local law and rigidity for unitary Brownian motion
Abstract: We establish high probability estimates on the eigenvalue locations of Brownian motion on the N-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are optimal up to arbitrarily small polynomial factors in N. Our results hold at the spectral edges (showing that the extremal eigenvalues are within $O(N^{-2/3+})$ of the edges of the limiting spectral measure), in the spectral bulk, as well as for times near 4 at which point the limiting spectral measure forms a cusp. Our methods are dynamical and are based on analyzing the evolution of the Borel transform of the empirical spectral measure along the characteristics of the PDE satisfied by the limiting spectral measure, that of the free unitary Brownian motion. Joint work with Arka Adhikari
Date
Wednesday February 15, 2023Location
Jeffery Hall, Room 319Wednesday, February 15th, 2023
Time: 12:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Somnath Pradhan (Queen's University)
Title: TBA
Abstract: TBA
Date
Wednesday February 8, 2023Location
Jeffery Hall, Room 319Wednesday, February 8th, 2023
Time: 12:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Zachary Selk (Queen's University)
Title: Trapezoid Rule for Rough Paths
Abstract: Rough paths theory is an alternative theory of solving stochastic differential equations to the classical Ito theory. Rough paths have two main advantages over Ito theory. First, it can be used to solve differential equations driven by more general processes than semi-martingales. Second, it can be used to solve differential equations in a pathwise way. Furthermore the solution map is continuous - that is, given two instances of driving signals that are close the solutions are also close.
The so-called "rough integral" is a standard Riemann-Stieltjes integral with an additional "correction term" which can be viewed as encoding a kind of "iterated integral" of the driving signal against itself. This correction term can be seen as unnatural. In this talk, we show for a wide class of Gaussian processes including the fractional Brownian motion one can simply use the trapezoid rule. Joint work with Yanghui Liu and Samy Tindel.
