Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Milen Yakimov (Northeastern University)

Milen Yakimov (Northeastern University)

Friday, January 29th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Milen Yakimov (Northeastern University)

Title: Noncommutative Discriminants.

Abstract: The notion of discriminant plays an important role in various algebraic, geometric and combinatorial settings. The discriminant of a noncommutative algebra is modeled on Dedekind's definition for algebraic number fields. The discriminants in the former class have many applications but have only been computed in few situations. We will present an introduction to this subject and will then describe three general theorems for computing discriminants of noncommutative algebras based on Poisson geometry, Representation Theory and Cluster Algebras, respectively. The three theorems can be applied to compute the discriminants of many families of algebras of wide interest: quantum matrices at roots of unity, quantum Weyl algebras, quantum Schubert cell algebras, algebras in noncommutative projective algebraic geometry and others. The talk is based on joint work with Kenneth Brown (Glasgow University), Bach Nguyen (Xavier University) and Kurt Trampel (University of Notre Dame).

Milen Yakimov is a Professor in the Department of Mathematics at Northeastern University. His research interests include noncommutative algebra, quantum groups, Poisson geometry, cluster algebras, representation theory and integrable systems. Before joining Northeastern University, he was the Michael F. and Roberta Nesbit McDonald Professor in the Department of Mathematics at the Louisiana State University. He became a Fellow of the American Mathematical Society in 2018.

Department Colloquium - Mohammad Farazmand (NC State)

Mohammad Farazmand (NC State University)

Friday, January 22nd, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Mohammad Farazmand (NC State University)

Title: Extreme Events: Dynamics, Prediction and Mitigation.

Abstract: A wide range of natural and engineering systems exhibit extreme events, i.e., spontaneous intermittent behavior manifested through sporadic bursts in the time series of their observables. Examples include ocean rogue waves, intermittency in turbulence, extreme weather patterns and epileptic seizure. Because of their undesirable impact on the system or the surrounding environment, the real-time prediction and mitigation of extreme events is of great interest. In this talk, I will discuss three aspects of extreme events. First, I introduce a variational method that unveils the mechanisms underpinning the formation of extreme events. Next, I show how this framework enables the data-driven, real-time prediction of extreme events. I demonstrate the application of this method with several examples, including the prediction of ocean rogue waves and the intermittent energy dissipation bursts in turbulent fluid flows. Finally, I will discuss a closed-loop adaptive control and a delay feedback control for mitigating extreme events.

Mohammad Farazmand is an assistant professor within the Department of Mathematics at North Carolina State University. He works on the fields of data-driven modeling and analysis of complex systems. He was previously a postdoctoral associate at the Massachusetts Institute of Technology and a J. Ford Postdoctoral Fellow at the Georgia Institute of Technology. He obtained his Ph.D. in 2014 from ETH Zurich under the supervision of George Haller.

Dynamics, Geometry, & Groups - Macarena Arenas (Cambridge)

Thursday, January 21st, 2021

Time: 1:30 p.m Place:

Speaker: Macarena Arenas (University of Cambridge)

Title: Linear isoperimetric functions for surfaces in hyperbolic groups.

Abstract: One of the main characterisations of word-hyperbolic groups is that they are the groups with a linear isoperimetric function. That is, for a compact 2-complex X, the hyperbolicity of its fundamental group is equivalent to the existence of a linear isoperimetric function for disc diagrams D -->X.
It is likewise known that hyperbolic groups have a linear annular isoperimetric function and a linear homological isoperimetric function. I will talk about these isoperimetric functions, and about a (previously unexplored) generalisation to all homotopy types of surface diagrams. This is joint work with Dani Wise.

Geometric Sports Analytics - Timothy Chan (U of T)

Wednesday, January 20th, 2021

Time: 2:00-3:30 p.m.  Place: Virtual Zoom Meeting

Speakers: Professor Timothy Chan of the University of Toronto

Title: spORts

Abstract: This talk attempts to put the OR in sports analytics. We will present applications of operations research methods such as robust and integer optimization, simulation, and Markov Decision Processes to decision problems in hockey, baseball and tennis.

Seminar Organizers: Catherine Pfaff & Daniel McBride

Information: Please email Catherine Pfaff for more information and to get the Zoom link.

Department Colloquium - Grace Y. Yi (University of Western Ontario)

Grace Y. Yi (University of Western Ontario)

Friday, January 15th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Grace Y. Yi (University of Western Ontario)

Title: Characterizing the Dynamic of COVID-19 with a New Epidemic Model.

Abstract: The mystery of the coronavirus disease 2019 (COVID-19) and the lack of effective treatment for COVID-19 have presented a strikingly negative impact on public health. While research on COVID-19 has been ramping up rapidly, a very important yet somewhat overlooked challenge is on the quality and unique features of COVID-19 data. The manifestations of COVID-19 are not yet well understood. The swift spread of the virus is largely attributed to its stealthy transmissions in which infected patients may be asymptomatic or exhibit only flu-like symptoms in the early stage. Due to the limited test resources and a good portion of asymptomatic infections, the confirmed cases are typically under-reported, error-contaminated, and involved with substantial noise. In this talk, I will discuss some issues related to faulty COVID-19 data and present a new model to describe the dynamic evolution of COVID-19. In addition, I will mention a website of COVID-19 Canada (https://covid-19-canada.uwo.ca/), developed by the team co-led by Dr. Wenqing He and myself, which provides a comprehensive and real-time visualization of the Canadian COVID-19 data.

Grace Y. Yi is a professor of the University of Western Ontario where she currently holds a Tier I Canada Research Chair in Data Science. She received her Ph.D. in Statistics from the University of Toronto in 2000 and then joined the University of Waterloo as a postdoctoral fellow (2000-2001), Assistant Professor (2001-2004), Associate Professor (2004-2010), Professor (2010-2019), and University Research Chair (2011-2018). Her research interests focus on developing methodology to address various challenges concerning Data Science, public health, cancer research, epidemiological studies, environmental studies, and social science. Her recent research has been centered around investigating machine learning and statistical methods to tackle problems concerning imaging data, missing data, measurement error in variables, causal inference, high dimensional data, survival data, and longitudinal data. She is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, and an Elected Member of the International Statistical Institute. She won the prestigious CRM–SSC Prize of the Statistical Society of Canada in 2010. She was a recipient of the University Faculty Award (2004-2009) granted by the Natural Sciences and Engineering Research Council of Canada. Her work with Xianming Tan and Runze Li won the Canadian Journal of Statistics Award for 2016. She has served the professions in various capacities. She was the Editor-in-Chief of The Canadian Journal of Statistics (2016-2018) as well as the President of the Biostatistics Section of the Statistical Society of Canada in 2016, and the Founder of the first chapter (Canada Chapter, established in 2012) of International Chinese Statistical Association (ICSA).

Dynamics, Geometry, & Groups - Hakan Doga (SUNY Buffalo)

Thursday, January 14th, 2021

Time: 1:30 p.m Place:

Speaker: Hakan Doga (SUNY Buffalo)

Title: A Combinatorial Description of the Knot Concordance Invariant Epsilon.

Abstract: Sitting at the intersection of 4-dimensional topology and knot theory, the knot concordance group is an important object in low-dimensional topology whose structure is not yet fully explored and understood. One approach to study knot concordance is to use knot Floer homology, introduced by Ozsvath-Szabo and Rasmussen independently in early 2000s, and the invariants obtained from this theory. In this talk, I will describe the knot concordance, introduce some basic definitions of the combinatorial knot Floer homology called the "grid homology", explain our method of computing the concordance invariant epsilon and talk about some results. This is a joint work with S. Dey.

Geometry & Representation - Souheila Hassoun (Sherbrooke)

Monday, November 30th, 2020

Time: 4:30p.m.  Place: Zoom

Speaker: Souheila Hassoun (Université de Sherbrooke)

Title: Jordan-Hölder exact categories

Abstract:  Exact categories goes back to the work of Yoneda and generalise the important and widely used notion of abelian categories. In a joint work with T. Brüstle and A. Tattar, we generalise the famous Jordan-Hölder theorem to the realm of Quillen exact categories.

Website details here: https://mast.queensu.ca/~georep/

Department Colloquium - Ian Frankel (Queen's University)

Ian Frankel (Queen's University)

Friday, November 27th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Ian Frankel (Queen's University)

Title: Invariant measures for straight line flows.

Abstract: We discuss the question of equidistribution of billiard trajectories in polygons. As it turns out, for polygons whose angles are rational, this is related to the geometry of a 1-parameter family of surfaces in a moduli space. We will describe how the possible measures with respect to which a billiard trajectory may equidistribute are constrained by this 1-parameter family of surfaces.

Ian Frankel is a Coleman Research Fellow within the Department of Mathematics and Statistics at Queen’s University. He obtained his Ph.D. in Mathematics from the University of Chicago in 2018. He was a Research Fellow at the Higher School of Economics and a Fields Postdoctoral Fellow at The Fields Institute for Research in Mathematical Sciences. He is mainly interested in geometry and topology and dynamical systems.

Dynamics, Geometry, & Groups - Hang Lu Su (ICMAT Madrid)

Thursday, November 26th, 2020

Time: 2:00 p.m Place:

Speaker: Hang Lu Su (ICMAT Madrid)

Title: Left-orderable groups and formal languages.

Abstract: I will introduce the notions of left-orderable groups, the topology on the space of left-orders, and formal language complexity with respect to the Chomsky hierarchy. I will give an idea of why it is intriguing to study left-orders using language complexity by introducing a toy example with the Klein bottle group. Finally, I will introduce some recent results concerning the closure properties of positive cone complexity. This work is joint with Yago Antolín and Cristóbal Rivas.

Statistics & Biostatistics - Brian Ling (Queen's University)

Tuesday, November 24th, 2020

Time: 1:00pm Place:

Speaker: Brian Ling (Queen's University)

Title: Nonparametric estimation for cross-sectional data

Abstract: Current duration data collected from cross-sectional sampling provides an alternative opportunity to estimate the survival function of the variable of interest in addition to prospective and retrospective designs. In this talk, we will first review the connection of current duration data with shape-constrained inference. While different nonparametric estimators for the underlying survival function have been proposed in the literature, some of their theoretical properties are missing. We will establish the asymptotic distributions of these estimators. Semiparametric models will also be discussed.

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