Date
Monday March 6, 2023Location
Jeffery Hall, Room 222Monday, March 6th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 222
Speaker: Thai Thanh Nguyen (McMaster University)
Title: Duality for Asymptotic Invariants
Abstract:
Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html
Date
Wednesday March 1, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, February 1st, 2023
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 & Zoom
Speaker: Calvin Fletcher
Title: Towards the affine toric variety of a polytope
Abstract: The purpose of this lecture will be to develop the geometric concepts required to define the affine toric variety of a polytope. We will study the relationship between the faces of a full dimensional polytope and the cones generated by their facet normals. We then define the normal fan of a polytope and provide some examples. Finally, we will briefly introduce the definition of an affine toric variety of a polytope.
Date
Monday February 27, 2023Location
Jeffery Hall, Room 319Monday, February 27th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Abhishek Bharadwaj (Queen's University)
Title: On some relations associated to special values of the digamma function
Abstract: A distribution relation is a relation of the form f(x) = \sum_{b=0}^{m-1}f((x+b)/m) for all numbers x and for all natural numbers m. These relations are known for the Bernoulli polynomials and for logarithm of Cyclotomic units. The above identity should be thought of obtaining a value of the function in a `lower level' from some values in the `higher level'. In this talk, we shall discuss some of the relations associated to the special values of the digamma function. This is a joint work with Ram Murty (work in progress).
Date
Friday March 3, 2023Location
Jeffery Hall, Room 234Friday, March 3rd, 2023
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Nasrin Altafi (Queen's University)
Title: On the shape of Hilbert functions of Gorenstein algebras
Abstract: The Hilbert function is a numerical invariant that measures the number of independent conditions for a given geometric object. A significant part of the beauty of Hilbert functions is derived from their ubiquity in commutative algebra and algebraic geometry. Characterizing the shape of the Hilbert function in Gorenstein algebras is a major problem in commutative algebra. A characterization of the Hilbert functions of the Artinian Gorenstein (AG) algebras with codimensions of less than four was provided in 1980. This characterization is no longer true for higher codimensions althouhg it characterizes the Hilbert functions of AG algebras with the so called "Lefschetz property”. The Lefschetz property concerns the rank of the multiplication map by a general linear form on a given Artinian algebra. The study of such properties originates from the Hard Lefschetz theorem, which was a breakthrough in algebraic topology and geometry. The Lefschetz properties are especially important in terms of their implications for the Hilbert function. During the last 25 years, investigations of these properties have been of great interest. Lefschetz properties encode information about the Artinian algebra and their Hilbert functions. I will attempt to provide an overview of this topic, as well as important results and questions that contribute to this subject.
Nasrin Altafi is a postdoctoral fellow at Queen's University who is supported by a Swedish Research Council grant. She received her Ph.D. from the KTH Royal Institute of Technology in Sweden. Before moving to Canada, she was a postdoctoral fellow at Copenhagen University. Nasrin’s research interests lie in commutative algebra and algebraic geometry as well as their interactions with combinatorics and computational algebra.
Date
Thursday February 16, 2023Location
Jeffery Hall, Room 118Thursday, February 16th, 2023
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: M. Ram Murty (Queen's University)
Title: Brain Networks and Graph Theory
Abstract: In the last 20 years neuroscience has adopted the language of graph theory to study brain networks.
In this talk, we give an introduction to this exciting development and indicate how graph theory can be used to study the "brain hubs" problem of neuroscience.
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
