Department of

Mathematics


Seminar Calendar
for Graduate analysis seminar events the year of Wednesday, September 13, 2017.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2017           September 2017          October 2017    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5                   1  2    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
 27 28 29 30 31         24 25 26 27 28 29 30   29 30 31            
                                                                   

Tuesday, April 11, 2017

3:00 pm in 241 Altgeld Hall,Tuesday, April 11, 2017

Equivalence of Quasiconvexity and Rank-One Convexity

Terry Harris   [email] (UIUC Math)

Abstract: In 1952 Morrey conjectured that quasiconvexity and rank-one convexity are not equivalent, for functions defined on m by n matrices. For two by two matrices this conjecture is still open. I will outline a proof that equivalence holds on the subspace of two by two upper-triangular matrices, which extends the result on diagonal matrices due to Müller. This is joint work with Bernd Kirchheim and Chun-Chi Lin.

Thursday, May 11, 2017

3:00 pm in 243 Altgeld,Thursday, May 11, 2017

The Complexity of Classifying Unitaries

Aristotelis Panagiotopoulos   [email] (UIUC Math)

Abstract: Classification problems occur in all areas of mathematics. Descriptive set theory provides methods for measuring the complexity of such problems. For example, using a technique developed by Hjorth, Kechris and Sofronidis proved that the problem of classifying all unitary operators of an infinite dimensional Hilbert space up to unitary equivalence is strictly more difficult than classifying graph structures on domain N up to isomorphism. In this talk I will review the basics from descriptive set theory and explain why the problem of classifying unitaries is so hard. Part of my talk will be based on recent joint work with Martino Lupini.

Friday, September 1, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 1, 2017

Organizational meeting

All A. Vus (UIUC)

Abstract: We will compare our schedules and find a regular time for the seminar. Cookies will be provided.

Friday, September 8, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 8, 2017

Life’s a blur, live on the edge

Derek Jung (UIUC)

Abstract: A focal problem in image processing is deblurring images and a common model for blurring images is convolution with a fixed kernel. I consider an integral operator arising from taking the blurred image of the edge of an opaque wall. I prove that the Tikhonov regularized problem for this operator is well-posed, which essentially means that one can invert the blurred image to the kernel continuously. This is joint work with Dr. Aaron Luttman and Dr. Kevin Joyce and was performed during a summer internship with National Security Technologies in Las Vegas. No background is necessary, but some knowledge of measure theory would be helpful.

Friday, September 15, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 15, 2017

Fun with Heisenberg

Matt Romney (UIUC)

Abstract: This is an expository talk on a fascinating mathematical object, the Heisenberg group. It is the simplest example of what could be termed a "non-commutative vector space". Yet despite its simple definition, many basic questions about its geometry are still open. The Heisenberg group arises in a variety of mathematical contexts, most notably quantum mechanics and complex analysis of several variables. This talk will give a hands-on introduction to the Heisenberg group, and indicate some of its recent applications.

Friday, September 22, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 22, 2017

Measurable Differentiable Structures and Nonbeddability into RNP spaces

Chris Gartland (UIUC)

Abstract: In 1999, Cheeger proved that doubling metric measure spaces admitting a Poincare inequality carry a 'measurable differentiable structure' with respect to which Lipschitz functions could be differentiated almost everywhere. A major consequence of this theorem is that if such a space were to biLipschitz embed into a finite dimensional normed space (or as was later proved, any RNP space), a generic point would have all of its tangent cones biLipschitz equivalent to some finite dimensional normed space. We'll outline the proof of this consequence and discuss its application to Carnot groups and inverse limits of graphs.

Friday, September 29, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 29, 2017

Unrectifiability Via Projections

Fernando Roman Garcia (UIUC)

Abstract: In the study of analysis on metric spaces, rectifiable sets are the appropriate analogue of smooth manifolds. Due to a celebrated theorem of Rademacher, we know rectifiable sets have a "sort of" almost-everywhere-differentiable structure with respect to which one can define approximate tangent planes and do calculus at almost every point. Classifying rectifiable or, on the other end of the spectrum, purely unrectifiable sets is not an easy task. In this talk we will see a certain classification of purely unrectifiable sets via orthogonal projections, will see how Fourier analysis plays a key role in this subject and will talk about how (if at all) similar classification can be apply to more general metric spaces, specifically the Heisenberg Group. Note: This talk will be expository, introductory and for the most part self-contained. No knowledge beyond a basic understanding of metric spaces and measure theory will be needed to follow along.

Friday, October 6, 2017

12:00 pm in 243 Altgeld Hall,Friday, October 6, 2017

Regularity Lemmata via Graph Theory and Analysis

Aubrey Laskowski (UIUC)

Abstract: I will be exploring some interesting connections between graph theory and analysis through versions of Szemerédi's regularity lemma. Szemerédi's lemma states that every large enough graph can be divided into near equipartitions such that edges between the partitions behave almost randomly. In the style of a 2007 paper by Lovász and Szegedy, I generalize this problem to the setting of stepfunctions on a Hilbert space then dive into the world of graphons, analytic objects which act as the limit to a sequence of dense graphs. No particular background needed in graph theory or analysis.

Friday, October 13, 2017

12:00 pm in 243 Altgeld Hall,Friday, October 13, 2017

The Determinant of the Laplacian in Geometric Analysis

Hadrian Quan (UIUC)

Abstract: In this talk I’ll introduce a few different types of Spectral Functions, and describe their use in geometry, culminating with an introduction to the Determinant of the Laplacian. I’ll spend some time trying to make sense of what this object could mean, especially since the eigenvalues of the laplacian accumulate at infinity. Zeta functions may be involved, but I promise the number $\frac{-1}{12}$ will be nowhere to be seen.

Friday, October 20, 2017

12:00 pm in 243 Altgeld Hall,Friday, October 20, 2017

Toeplitz Operators and Bott Periodicity

Timothy Drake (UIUC)

Abstract: The Toeplitz operators are a class of bounded operators on the Hardy space $H^2$, which may be thought of as infinite-dimensional analogues of Toeplitz matrices. They form a $C^*$-algebra known as the Toeplitz algebra, which plays a central role in the theory of $C^*$-algebras as the "universal $C^*$-algebra generated by a single isometry". I will discuss the properties of this algebra and its relation to $K$-theory, and use it to sketch a proof of the Bott Periodicity Theorem for $C^*$-algebras.

Friday, October 27, 2017

12:00 pm in 243 Altgeld Hall,Friday, October 27, 2017

Universal Taylor series

Maria Siskaki

Abstract: A series of the form $Σa_n z^n, z \in \mathbb{C}$, with radius of convergence $R=1$, is called a Universal Taylor series if for each compact set $K$ which is disjoint from the unit disc and has connected complement, and each function $h$ in $A(K)$, there exists a subsequence of the sequence of partial sums of the series that approximates $h$ uniformly on $K$. In other words, the series diverges so badly outside the unit disc, that it approximates any reasonably good function defined on any reasonably good set. In this talk I will prove the existence of Universal Taylor series and discuss some of their properties.

Friday, November 3, 2017

12:00 pm in 245 Altgeld Hall,Friday, November 3, 2017

Scattered Results on the Bishop-Phelps-Bollobás Property

Kimberly Duran (UIUC)

Abstract: The Bishop-Phelps-Bollobás property for a space of operators is a stronger version of having a dense subset of norm-attaining operators. This is a topic in functional analysis with a many scattered results, and as yet few large unifying problems. I'll discuss the historical development and some of the known positive and negative results in this expository talk.

Friday, November 10, 2017

12:00 pm in 243 Altgeld Hall,Friday, November 10, 2017

Lipschitz Algebras

Chris Gartland (UIUC)

Abstract: Through the theory of Gelfand duality, a compact Hausdorff space $X$ may be recovered purely from its commutative C*-algebra of continuous $\mathbb{C}$-valued functions, $C(X)$. In the case where $X$ carries a metric $d$, $C(X)$ alone is not sufficient to determine $d$, as a generic metrizable space carries many mutually inequivalent metrics. However, the commutative Banach *-algebra of $\mathbb{C}$-valued Lipschitz functions, Lip$(X,d)$, is sufficient to recover $d$ up to biLipschitz equivalence, and we'll outline the proof of this fact. We will also discuss possible abstract characterizations of the commutative Banach *-algebras isomorphic to Lip$(X,d)$ for some $(X,d)$.

Friday, December 1, 2017

12:00 pm in 243 Altgeld Hall,Friday, December 1, 2017

Dynamical Systems via Machine Learning

Lan Wang (UIUC)

Abstract: Machine learning has become an important technique to understand and predict the trends of large volume of data. While most machine learning models are static, static is hardly the case in real life. We need to create dynamical models by generalizing from past experience and results. In this talk, I will explore the usages of dynamical systems in machine learning. The talk will be divided into two parts. First, I will focus on the Kalman filter, a famous Bayesian model permitting exact inference in a discrete dynamical system, and its extensions. Then, I will discuss how to use continuous dynamical systems as a tool for machine learning, especially for deep neural networks. Some of the results are from my previous internship experience.