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Math & Stats Department Colloquium

Friday, March 10th, 2023

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

Speaker: Jose Perea (Northeastern)

Title: The underlying Topology of Data

Abstract: Topology is the branch of mathematics concerned with shapes and their spatial properties. In this talk I’ll show how several ideas from classic algebraic topology – like cohomology, classifying spaces and vector bundles – can be used in machine learning tasks such as dimensionality reduction, time series analysis and data alignment.

Dr. Perea earned his Ph.D. in Mathematics from Stanford University in 2011, and a B.Sc. in Mathematics from Universidad del Valle (Summa cum laude and Valedictorian) in 2006. He was a postdoc in the depart- ment of Mathematics at Duke from 2011 to 2015, and a long term visitor of the Institute for Mathematics and its Applications (IMA) at the University of Minnesota during the Fall of 2014. In August of 2015 he joined Michigan State University as an Assistant Professor with joint appointments in the department of Computational Mathematics, Science and Engineering (CMSE), and the department of Mathematics. Dr. Perea moved to Northeastern University in the Fall of 2021 as an Associate Professor in the department of Mathematics and the Khoury College of Computer Sciences.

The work of Dr. Perea has been supported by grants from DARPA, the National Science Foundation, the Center for Business and Social Analytics, and an NSF CAREER award.

Math Club

Thursday, March 2nd, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Greg Smith (Queen's University)

Title: Mathematical Mistakes

Abstract: What kinds of mistakes do mathematicians make?

In this talk, we will explore a partial taxonomy of mathematical errors.  Using some infamous examples, we hope to gain historical insight, improve our self-awareness, and generally be entertained.

Algebra & Geometry Seminar

Monday, March 13th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 222

Speaker: Abdul Zalloum (University of Toronto)

Title: Metrics on mapping class groups

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Algebra & Geometry Seminar

Monday, 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

Curves Seminar

Wednesday, 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.

Number Theory Seminar

Monday, 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).

Math & Stats Department Colloquium

Friday, 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.

Math Club

Thursday, 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.

Algebra & Geometry Seminar

Monday, 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

Math & Stats Department Colloquium

Friday, 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.