Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Jorge Cortes (UC San Diego)

Jorge Cortes (University of California, San Diego)

Friday, April 5th, 2019

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

Speaker: Jorge Cortes (University of California, San Diego)

Title: The Role of Network Structure in Controlling Complex Networks.

Abstract: Controllability of complex network systems is an active area of research at the intersection of network science, control theory, and multi-agent coordination, with multiple applications ranging from brain dynamics to the smart grid and cyber-physical systems. The basic question is to understand to what extent the dynamic behavior of the entire network can be shaped by changing the states of some of its subsystems, and decipher the role that network structure plays in achieving this. This talk examines this question in two specific instances: characterizing network controllability when control nodes can be scheduled over a time horizon and hierarchical selective recruitment in brain networks. Regarding controllability, we show how time-varying control schedules can significantly enhance network controllability over fixed ones, especially when applied to large networks. Through the analysis of a novel scale-dependent notion of nodal centrality, we show that optimal time-varying scheduling involves the actuation of the most central nodes at appropriate spatial scales. Regarding hierarchical selective recruitment, we examine network mechanisms for selective inhibition and top-down recruitment of subnetworks under linear-threshold dynamics. Motivated by the study of goal-driven selective attention in neuroscience, we build on the characterization of key network dynamical properties to enable, through either feedforward or feedback control, the targeted inhibition of task-irrelevant subnetworks and the top-down recruitment of task-relevant ones.

Jorge Cortes is a Professor with the Department of Mechanical and Aerospace Engineering at the University of California, San Diego. He received his Ph.D. degree in engineering mathematics from the Universidad Carlos III de Madrid, Spain, in 2001 and held postdoctoral positions at the University of Twente, The Netherlands, and at the University of Illinois at Urbana-Champaign, USA. He was an Assistant Professor with the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz from 2004 to 2007. He is an IEEE Fellow and is currently its Director of Operations and an elected member (2018-2020) of its Board of Governors. He has received many prestigious award including the NSF CAREER award in 2006, the 2006 Spanish Society of Applied Mathematics Young Researcher Prize, the 2008 IEEE Control Systems Outstanding Paper Award, the 2009 SIAM Review SIGEST selection from the SIAM Journal on Control and Optimization, and the 2012 O. Hugo Schuck Best Paper Award in the Theory category. His current research interests include distributed control and optimization, network neuroscience, reasoning and decision making under uncertainty, resource-aware control, and multi-agent coordination in robotic, power, and transportation networks.

Math Club - Francesco Cellarosi (Queen's University)

Thursday, April 4th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Francesco Cellarosi (Queen's University)

Title: The irrationality of $\zeta(3)$.

Abstract:  This talk will discuss the famous theorem by R. Apéry who showed in 1978 that $\zeta(3)$ is irrational.
We will see a proof of this fact, due to F. Beuker in 1979, which only uses calculus.

Geometry & Representation - Ba Nguyen (Queen's University)

Monday, April 1st, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Ba Nguyen (Queen's University)

Title: A Combinatorial Model for Detecting Cluster Variables of Type D Cluster Algebras

Abstract:  Perfect Matchings of a Snake Diagram, which was developed by G. Musiker, R. Schiffler and L. Williams, can be employed to compute cluster variables of a type D cluster algebra. Based on that model we have developed a new model called Globally Compatible Sequence. In this talk, we will discuss how to find cluster variables using this model. To have a better understanding of those cluster variables, description of their denominator vectors will also be introduced.

Department Colloquium - Carolyn Gordon (Dartmouth College)

Carolyn Gordon (Dartmouth College)

Friday, March 29th, 2019

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

Speaker: Carolyn Gordon (Dartmouth College)

Title: Decoding geometry and topology from the Steklov spectrum of orbisurfaces.

Abstract: The Dirichlet-to-Neumann or "voltage-to-current" operator of, say, a surface $M$ with boundary is a linear map $C^\infty(\partial M)\to C^\infty(\partial M)$ that maps the Dirichlet boundary values of each harmonic function $f$ on M to the Neumann boundary values of $f$. The spectrum of this operator is discrete and is called the Steklov spectrum. The Dirichlet-to-Neumann operator also generalizes to the setting of orbifolds, e.g., cones. We will address the extent to which the Steklov spectrum encodes the geometry and topology of the surface or orbifold and, in particular, whether it recognizes the presence of orbifold singularities such as cone points.

This is joint work with Teresa Arias-Marco, Emily Dryden, Asma Hassannezhad, Elizabeth Stanhope and Allie Ray.

Prof. Gordon is an expert in spectral geometry. She obtained her PhD from Washington University in 1979, then went to the Technion institue and held positions at Lehigh University and Washington University before moving to Dartmouth where she is currently the Benjamin Cheney Professor of Mathematics.
Prof. Gordon was awarded an AMS Centennial Fellowship in 1990, the MAA Chauvenet prize in 2001 and was the 2010 Noether Lecturer. In 2012, she became a fellow of both the AMS and the American Association for the Advancement of Science. In 2017, she was selected to be a fellow of the AWM in the inaugural class.

Number Theory - Tariq Osman (Queen's University)

Tuesday, March 26th, 2019

Time: 1:00-2:00 p.m.  Place: Jeffery Hall 422

Speaker: Tariq Osman (Queen's University)

Title: Counting Integer Points on Vinogradov's Quadric.

Abstract: Consider the variety defined by the pair of equations $x_1 + x_2 + x_3 = y_1 + y_2 + y_3$ and $ x_1^2 + x_2^2 + x_3^2 = y_1^2 + y_2^2 + y_3^2$, known as Vinogradov's quadric. Following a brief historical overview and a few motivational remarks, we will derive an asymptotic formula (due to Ragovskya) for the number of integer points on Vinogradov's quadric in a large box.

Dynamics, Geometry, & Groups - Alessandro Portaluri (U of Torino)

Friday, March 22nd, 2019

Time: 10:30 a.m Place: Jeffery Hall 102

Speaker: Alessandro Portaluri (University of Torino, Italy)

Title: Visiting Kepler with a couple of symplectic friends.

Abstract: Starting from the classical planar Kepler problem, by using the conservation law of the angular momentum, we reduce the problem to a one degree of freedom singular problem. Thanks to this reduction and after a suitable time scaling we show that, for negative energy, the orbit is an ellipse. Finally, by using a refined version of the Conley-Zehnder intersection index , we give a homotopic classification of all bounded motions.

Department Colloquium - Maksym Radziwill (Caltech)

Maksym Radziwill (California Institute of Technology)

Friday, March 22nd, 2019

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

Speaker: Maksym Radziwill (California Institute of Technology)

Title: Recent progress in multiplicative number theory.

Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to $L$-functions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments. An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance $n$ and $n+ 1$. A central conjecture making this precise is the Chowla-Elliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis. However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.

Maksym Radziwill graduated from McGill University in Montreal in 2009, and in 2013 took a PhD under Kannan Soundararajan at Stanford University in California. In 2013-2014, he was at the Institute for Advanced Study in Princeton, New Jersey as a visiting member, and in 2014 became a Hill assistant professor at Rutgers University. In 2016, he became an assistant professor at McGill. In 2018, he became Professor of Mathematics at Caltech.

Math Club - Ivan Dimitrov (Queen's University)

Thursday, March 21st, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Ivan Dimitrov (Queen's University)

Title: Why 0.499999999992646 does not equal 12.

Abstract:  We will see why

  • $\int_{0}^\infty \frac{\sin x}{x} \,dx = \pi/2,$
  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3}\, dx = \pi/2, $

… and so on all the way to

  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13}\, dx = \pi/2, $

However,

  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13} \cdot \frac{\sin x/15}{x/15} \,dx < \pi/2, $

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