Department of

Mathematics


Seminar Calendar
for Graduate Student Colloquium events the year of Thursday, July 2, 2020.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, February 5, 2020

4:00 pm in 245 Altgeld Hall,Wednesday, February 5, 2020

Displays of Polish Isometry Groups in Banach Lattices

Mary Angelica Gramcko-Tursi

Abstract: A Polish group $G$ is displayable in a Banach lattice $(X, \|\cdot \|)$ if there exists a group homomorphism $\rho$ from $G$ into the lattice isometries of $X$ such that 1) $G$ is homeomorphic to $\rho(G)$, and 2) $X$ can be renormed with an equivalent lattice norm $\|| \cdot |\|$ so that $\rho(G)$ is the group of lattice isometries on $(X, \| | \cdot | \| )$. When is a group $G$ displayable in a Banach lattice $X$? This question has been explored in the context of Banach spaces and surjective linear isometries. In this talk based on ongoing work, we first survey some the known results and techniques for displays in Banach spaces to provide context. We then prove displayability results for certain classes of Banach lattices. In particular, if $X$ is either order continuous or an $AM$ space, $X$ can be renormed using various techniques, so that the identity is the only lattice isometry on $X$. Finally, we expand on these techniques to give general conditions sufficient for $G$ to be a display on $X$. This talk will be accessible to grad students of all levels.

Monday, March 2, 2020

4:00 pm in 245 Altgeld Hall,Monday, March 2, 2020

Linear Analysis on Singular Spaces

Hadrian Quan

Abstract: As an undergraduate, one may be introduced to the 3 classic linear differential equations: Laplaceís equation, the heat equation, and the wave equation. Simply trying to solve these equations in different coordinate systems leads to a zoo of different solutions; such variation reflects the strong connection between the geometry of a space, and the behavior of solutions to these PDE on that space. Passing from Euclidean space to more general manifolds, these three equations can be studied whenever our manifold is equipped with the geometric structure of a Riemannian metric. In this talk I will highlight a few of the many surprising theorems exhibiting this connection between the geometry and topology of a manifold and the behavior of solutions to the Laplace, heat, and wave equation. Time permitting, Iíll highlight recent joint work with Pierre Albin of some new phenomena on certain singular spaces.

Wednesday, April 1, 2020

4:00 pm in 245 Altgeld Hall,Wednesday, April 1, 2020

A family of number-theoretic directed graphs on the integers

Dana Neidinger