Department of

# Mathematics

Seminar Calendar
for Graduate Analysis Seminar events the year of Monday, October 26, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2020          October 2020          November 2020
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Friday, January 24, 2020

3:00 pm in 347 Altgeld Hall,Friday, January 24, 2020

#### Organizational Meeting

###### Kesav Krishnan (UIUC Math)

Abstract: This organizational meeting will be to decide on a schedule of speakers. All are welcome

Friday, January 31, 2020

3:00 pm in 347 Altgeld Hall,Friday, January 31, 2020

#### Indroduction to Non Commutative Probability

###### Kesav Krishnan (UIUC Math)

Abstract: In this talk I will introduce Non Commutative Probability Theory, and highlight some of its uses in classical Probability, such as the study of random matrices. In particular, motivation of Wigner's semi-circle law as the non commutative analog of the Central Limit Theorem.

Friday, February 7, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 7, 2020

#### Indroduction to Non Commutative Probability Part 2

###### Kesav Krishnan (UIUC Math)

Abstract: I will continue the talk from last friday, on the Introduction to Non Commutative Probability. In this talk, I will focus on limit laws, in particular the non commutative CLT and the universality of the semi-circle law.

Friday, February 14, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 14, 2020

#### An Introduction to $L^2$ Cohomology

###### Gayana Jayasinghe (UIUC Math)

Abstract: We'll see how we can construct quasi isometry invariants and some conformal invariants with function spaces and operators on manifolds (and some more general spaces), and how we can use analysis to study geometric structures

Friday, February 28, 2020

3:00 pm in 347 Altgeld Hall,Friday, February 28, 2020

#### Eigenvalues on Forms

###### Xiaolong Han (UIUC Math)

Abstract: Recently there has been a growing interest in eigenvalues on forms. It is much more complicated than eigenvalues on functions but can detect finer geometry. It has applications in detecting length of axes of John ellipsoid of convex body, relating Monopole Floer homology to hyperbolic geometry, and commutator length in hyperbolic geometry. In this talk we will show some basic theory and definitions for eigenvalues on forms, and then provide some intuition for the geometry and applications.

Friday, March 6, 2020

3:00 pm in 347 Altgeld Hall,Friday, March 6, 2020

#### Screened Sobolev Spaces

###### David Altizio (UIUC Math)

Abstract: TBA

Friday, August 28, 2020

1:00 pm in Zoom link sent to mailing list,Friday, August 28, 2020

#### Organizational Meeting

Abstract: We will discuss what time should the seminar happen, as well as who is going to give a talk when. Email either one of the organizers (ekc3(at)illinois.edu, kesavsk2(at)illinois.edu) if you wish to be added to the mailing list and/or to receive the meeting's link and password.

Friday, September 4, 2020

1:00 pm in Zoom,Friday, September 4, 2020

#### To Be Announced

###### Kesav Krishnan (UIUC Math)

Abstract: TBA

Friday, September 11, 2020

1:00 pm in Zoom,Friday, September 11, 2020

#### Complex dynamics and linearization

###### Stathis Chrontsios (UIUC Math)

Abstract: Complex dynamics is the study of iteration of either rational functions from the Riemann sphere into itself or entire functions. Fatou and Julia sets play a main role in that study. Their definitions will be given, as well as a few examples and properties. Last but not least, connections between complex dynamics, number theory and linearization will be discussed.

Friday, September 18, 2020

1:00 pm in Zoom,Friday, September 18, 2020

#### Positive Commutators, Propagation of Singularities, and trapping

###### Hadrian Quan   [email] (UIUC Math)

Abstract: In this talk I’ll describe the method of positive commutators, which is a flexible technique (=works on a manifold) for proving estimates about solutions of linear PDEs. Positive commutator estimates are useful for proving results about hyperbolic equations like the wave equation, or more generally any equations which involve a “flow”, by relating properties of solutions to the trajectories of an associated classical dynamical system. In particular they can give quantitative meaning to mysterious statements like “solutions of the wave equation propagate along light-cones.”

Friday, September 25, 2020

1:00 pm in Zoom link sent to mailing list,Friday, September 25, 2020

#### To Be Announced

###### Mary Angelica Gramcko-Tursi   [email] (UIUC Math)

Abstract: TBA

Friday, October 2, 2020

1:00 pm in Zoom,Friday, October 2, 2020

#### To Be Announced

###### Gayana Mahaarachchige Sarajakumara Jayasinghe (UIUC Math)

Abstract: TBA

Friday, October 9, 2020

1:00 pm in Zoom,Friday, October 9, 2020

#### To Be Announced

###### Ryan Mitchell McConnell (UIUC Math)

Abstract: TBA

Friday, October 16, 2020

1:00 pm in Zoom,Friday, October 16, 2020

#### To Be Announced

###### Dimitrios Diamantidis (Indiana University - Math)

Abstract: TBA

Friday, October 30, 2020

1:00 pm in Zoom,Friday, October 30, 2020

#### Permutable Quasiregular maps

###### Athanasios Tsantaris   [email] (University of Nottingham - Math)

Abstract: Do commuting holomorphic maps have the same Julia set? This question was first asked by Fatou and Julia around 1920 in their attempts to classify commuting rational maps. For rational maps the answer is affirmative but for transcendental entire maps the question is still open. In this talk we will first discuss the progress to the problem for transcendental entire maps over the years and then we shall describe generalizations of those results in the setting of quasiregular maps which are higher dimensional analogues of holomorphic maps.

Friday, November 6, 2020

1:00 pm in Zoom,Friday, November 6, 2020

#### Maximization of the second Laplacian Eigenvalue on the sphere

###### Hanna Kim (UIUC Math)

Abstract: I will explain a simplified approach to proving that the upper bound of the second (nonzero) eigenvalue of the Laplacian operator on the sphere can be maximized by considering a sequence of metrics. This sequence of metrics is going to that of 2-disjoint spheres with the same size. We construct trial functions using energy minimization which goes back to Szeg\"{o} and Weinberger.

Friday, November 13, 2020

1:00 pm in Zoom,Friday, November 13, 2020

#### Cyclicity preserving operators

###### Jeet Sampat   [email] (Washington University in St Louis - Math)

Abstract: For certain spaces of analytic functions in several complex variables, we will show that bounded linear operators that preserve shift-cyclic functions (i.e. Tf is shift-cyclic whenever f is shift-cyclic) are necessarily weighted composition operators. Examples of spaces for which this result holds true consist of the Hardy space, Dirichlet type spaces, Drury-Arveson space etc. In the case of Hardy spaces we will show that this condition is also sufficient. That is, all bounded weighted composition operators preserve cyclic functions in the Hardy spaces.