Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Data Science Applied Research & Education Seminar

Dr. Margaret E. Roberts Associate Professor Department of Political Science and the Halıcıoğlu Data Science Institute University of California, San Diego

Monday, December 7th, 2020

Time: 3:00-4:00p.m.  Place: Online (register)

Speaker: Dr. Margaret E. Roberts
Associate Professor
Department of Political Science and the Halıcıoğlu Data Science Institute
University of California, San Diego

Title: Resilience to Online Censorship

Free Event | All Welcome | Register Here

Abstract: 
To what extent are Internet users resilient to online censorship? When does censorship influence consumption of information and when does it create backlash? Drawing on data reflecting censorship evasion of the Great Firewall of China, I examine the extent to which individuals affected by censorship seek out ways to route around it. Using censorship events of Wikipedia and Instagram and crisis events like the outbreak of COVID, I examine how changes in the censorship and political environment influence censorship evasion. I find that crisis, as well as censorship of very popular and addictive websites, can create incentives for censorship evasion that in turn provides a gateway to long censored and sensitive political information. But, in the absence of a strong incentive to jump the wall, censorship events cut off access not only to political information, but also to opportunities for exploration and learning. Based on joint work with Jennifer Pan, Will Hobbs, Keng-Chi Chang, and Zachary Steinert-Threlkeld.

Profile: 
Dr. Roberts is Associate Professor in the Department of Political Science and the Halıcıoğlu Data Science Institute at the University of California, San Diego. She is also part of the Omni-Methods Group. Her research interests lie in the intersection of political methodology and the politics of information, with a specific focus on methods of automated content analysis and the politics of censorship and propaganda in China. Roberts received a PhD from Harvard in Government (2014), a MS from Stanford in Statistics (2009), and BA from Stanford in International Relations and Economics (2009). Much of her research uses social media, online experiments, and large collections of texts to understand the influence of censorship and propaganda on access to information and beliefs about politics. Her book, Censored: Distraction and Diversion Inside China’s Great Firewall, published by Princeton University Press in 2018, was listed as one of the Foreign Affairs Best Books of 2018, was honoured with the Goldsmith Book Award, and has been awarded the Best Book Award in the Human Rights Section and Information Technology and Politics Section of the American Political Science Association. She also holds a Chancellor’s Associates Endowed Chair at UCSD.

ARES is a collaboration between CANSSI Ontario and its partner universities.

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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.

Department Colloquium - Nicolas Fraiman (U of North Carolina)

Nicolas Fraiman (University of North Carolina)

Friday, November 20th, 2020

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

Speaker: Nicolas Fraiman (University of North Carolina)

Title: Stochastic Recursions on Random Graphs.

Abstract: We study a family of Markov processes on directed graphs where the values at each vertex are influenced by the values of its inbound neighbors and by independent fluctuations either on the vertices themselves or on the edges connecting them to their inbound neighbors. Typical examples include PageRank and other information propagation processes. Assuming a stationary distribution exists for this Markov chain, our goal is to characterize the marginal distribution of a uniformly chosen vertex in the graph. In order to obtain a meaningful characterization, we assume that the underlying graph is either a directed configuration graph or an inhomogeneous random digraph, both of which are known to converge, in the local weak sense, to a marked Galton-Watson process. We prove that the stationary distribution on the graph converges in a Wasserstein metric to a function of i.i.d. copies of the special endogenous solution to a branching distributional fixed-point equation. This is joint work with Mariana Olvera-Cravioto and Tzu-Chi Lin.

Nicolas Fraiman is an Assistant Professor in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He obtained his Ph.D. from McGill University in 2013. He was a Postdoctoral Fellow at the University of Pennsylvania and Harvard University. He works on the probabilistic analysis of random structures, stochastic dynamics, randomized algorithms and combinatorial statistics.

Department Colloquium - Yaiza Canzani (U of North Carolina)

Yaiza Canzani (University of North Carolina)

Friday, November 13th, 2020

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

Speaker: Yaiza Canzani (University of North Carolina)

Title: Eigenfunction concentration via geodesic beams.

Abstract: A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction concentration respond to the background dynamics of the geodesic flow. In collaboration with J. Galkowski, we developed a framework to approach this problem that hinges on decomposing eigenfunctions into geodesic beams. In this talk, I will present these techniques and explain how to use them to obtain quantitative improvements on the standard estimates for the eigenfunction's pointwise behavior, Lp norms, and for both pointwise and integrated Weyl Laws. One consequence of this method is a quantitatively improved Weyl Law for the eigenvalue counting function on all product manifolds.

Yaiza Canzani is an Assistant Professor in the Department of Mathematics at the University of North Carolina at Chapel Hill. She was awarded a Sloan Research Fellowship in 2018. Before joining UNC, Prof. Canzani was a Benjamin Peirce Fellow at Harvard University and a member of the Institute for Advanced Study. She obtained her Ph.D. from McGill University in 2013 under the supervision of Dmitry Jakobson and John Toth. She works on geometric analysis and spectral theory.

Department Colloquium - Florian Richter (Northwestern University)

Florian Richter (Northwestern University)

Friday, November 6th, 2020

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

Speaker: Florian Richter (Northwestern University)

Title: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions.

Abstract: One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases. This naturally leads to a formulation of an extended form of Sarnak's Mobius randomness conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.

Florian Richter is a Boas Assistant Professor in the Department of Mathematics at Northwestern University. He received his Ph.D. from The Ohio State University in 2018 under the supervision of Vitaly Bergelson. He received The Elizabeth Clay Howald Presidential Fellowship and Louise B.C. Vetter award for excellence in research from Ohio State. He works on dynamical systems, combniatorics and number theory.

Department Colloquium - Emine Yildirim (Queen’s University)

Emine Yildirim (Queen’s University)

Friday, October 23rd, 2020

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

Speaker: Emine Yildirim (Queen’s University)

Title: Graphs and Combinatorics in Representation Theory of Algebras.

Abstract: Representation theorists of finite dimensional algebras often use quivers, also known as directed graphs, and many other combinatorial tools associated with these quivers. This is because we understand the module category of algebras via representation of quivers. On the other hand, we also capture the beautiful combinatorics of cluster algebras via the same representation theory. In this talk, I will outline how this machinery works along with some recent results on Cluster Categories we obtained joint with Charles Paquette using the combinatorics and representations theory of quivers.

Emine Yildirim is a Coleman Research Fellow within the Department of Mathematics and Statistics at Queen’s University. She obtained her Ph.D. in Mathematics from the Universite du Quebec a Montreal in 2018. She is mainly interested in representation theory of algebras, specifically path algebras, incidence algebras, and their representations. She also works on cluster algebras, their categorification and related combinatorics.

Department Colloquium - Rafael Potrie (U de la Republica-Uruguay)

Rafael Potrie (Universidad de la Republica-Uruguay)

Friday, October 16th, 2020

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

Speaker: Rafael Potrie (Universidad de la Republica-Uruguay)

Title: Anosov flows and the fundamental group.

Abstract: The hairy ball theorem says that a vector field in the sphere must have some singularity. How does the dynamics interact with the topology of the underlying manifold in higher dimensions? We will discuss some instances of this question for dynamics in 3-manifolds, featuring a beautiful result due to Margulis and Plante-Thurston. Time permitting, we will touch upon more recent developments on the interactions between the topology and dynamics in 3 dimensions.

Rafael Potrie is an Associate Professor at the Universidad de la Republica-Uruguay. He obtained his Ph.D. in Mathematics from Universite Paris 13/Universidad de la Republica-Uruguay in 2012. He was an invited speaker of the Dynamical Systems session at the International Congress of Mathematicians (ICM) in 2018. His research mainly concerns the topological classification of partially hyperbolic systems in three-dimensional manifolds and its dynamical consequences. Other interests include smooth dynamics, ergodic theory, discrete subgroups of Lie groups, and the geometry of foliations and laminations.

Department Colloquium - Farouk Nathoo (University of Victoria)

Farouk Nathoo  (University of Victoria)

Friday, October 9th, 2020

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

Speaker: Farouk Nathoo (University of Victoria)

Title: Spatial Statistical Modeling for Neuroimaging Data.

Abstract: I will describe three projects involving the analysis of neuroimaging data and the development of hierarchical spatial Bayesian models for each. In the first, we develop an approach for determining the location and dynamics of brain activity from combined magnetoencephalography and electroencephalography data. The resulting inverse problem is ill-posed and we propose a distributed solution based on a Bayesian spatial finite mixture model that incorporates the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states. In the second project, we consider statistical modelling of functional magnetic resonance imaging (fMRI) data which is challenging in part as the data are both spatially and temporally correlated. Motivated by an event‐related fMRI experiment, we propose a novel hierarchical Bayesian model with automatic selection of the auto‐regressive orders of the noise process that vary spatially over the brain. In the third project, we develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative, where the objective is to examine the association between images of volumetric and cortical thickness values summarizing the structure of the brain as measured by magnetic resonance imaging (MRI) and a set of 486 SNPs from 33 Alzheimer's Disease (AD) candidate genes obtained from 632 subjects. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data and we develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We compare the new spatial model to an existing non-spatial model in our motivating application.

Department Colloquium - Elliot Paquette (McGill University)

Elliot Paquette (McGill University)

Friday, October 2nd, 2020

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

Speaker: Elliot Paquette (McGill University)

Title: Random perturbations of non-normal matrices.

Abstract: Suppose one wants to calculate the eigenvalues of a large, non-normal matrix. For example, consider the matrix which is 0 in most places except above the diagonal, where it is 1. The eigenvalues of this matrix are all 0. Similarly, if one conjugates this matrix, in exact arithmetic one would get all eigenvalues equal to 0. However, when one makes floating point errors, the eigenvalues of this matrix are dramatically different. One can model these errors as performing a small, random perturbation to the matrix. And, far from being random, the eigenvalues of this perturbed matrix nearly exactly equidistribute on the unit circle of the complex plane. This talk will give a probabilistic explanation of why this happens and discuss the general question: how does one predict the eigenvalues of a large, non-normal, randomly perturbed matrix?

Elliot Paquette is an Assistant Professor within the Department of Mathematics and Statistics at McGill University. He obtained his Ph.D.~in Mathematics from the University of Washington in 2013. He was an NSF Postdoctoral Fellow at the Weizmann Institute of Science from 2013-2016, and an Assistant Professor at the Ohio State University from 2016-2020. His research is in probability theory, with a focus on random matrix theory and on problems with geometric and topological inspirations.

Department Colloquium - Abdalrazzaq Zalloum (Queen's)

Abdalrazzaq Zalloum  (Queen's University)

Friday, September 25th, 2020

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

Speaker: Abdalrazzaq Zalloum (Queen's University)

Title: Negative curvature in geometric group theory.

Abstract: Geometric group theory studies the interplay between the algebraic/combinatorial properties of infinite groups and the geometries of the spaces on which they act. A naive example of this phenomena is the following theorem: "An infinite group is free if and only if it admits a free action on some tree". In the previous theorem, the geometric property of the tree containing no loops informed the algebraic/combinatorial property of the group being free and vice versa; this is a theme in geometric group theory. A metric space $X$ is said to be hyperbolic if there exists a number $\delta$ such that for any geodesic triangle in $X$, the union of the {$\delta$-nbhd} of any two of its three sides contains the third, see the attached image. Group actions on hyperbolic spaces tend to be particularly informative. A fundamental (and almost defining) property of hyperbolic spaces is that infinite geodesics satisfy a \textit{local to global} property: to check whether an infinite path is a geodesic in $X$, you need only to check that in uniformly small windows. Given a nice action of an infinite group $G$ on a hyperbolic space $X$, Cannon showed that the local-to-global property of geodesics in $X$ is reflected in the combinatorial structure of $G$. In particular, he observed that the local-to-global property of $X$ is inherited by $G$ in the sense that all the combinatorial and growth information of the \textbf{infinite} group $G$ can be encoded using only a $\textbf{finite}$ amount of data: a finite graph. I will discuss recent work where we study groups acting on spaces satisfying a similar local-to-global property, and we will see the interplay between the geometric local-to-global properties of the space, and the combinatorial structure of the acting group. Some of the results I will discuss are joint with Cordes, Russell and Spriano.

Abdalrazzaq Zalloum is a Coleman post-doctoral fellow within the Department of Mathematics and Statistics at Queen's University, working with Thomas Barthelmé and Francesco Cellarosi. He obtained his Ph.D. in Mathematics from the SUNY Buffalo in 2019. He is mainly interested in geometric group theory, which studies the interplay between the algebraic structures of groups and the geometries of the spaces on which they act.

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