Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, February 18, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 18, 2016

11:00 am in 241 Altgeld Hall,Thursday, February 18, 2016

#### The proof of Vinogradov's Mean Value Theorem

###### Ciprian Demeter (Indiana University Bloomington)

Abstract: I will present some history, implications to number theory and elements of our proof of VMVT. Joint work with Jean Bourgain and Larry Guth.

11:00 am in 345 Altgeld Hall,Thursday, February 18, 2016

#### T-duality and iterated algebraic K-theory

###### John Lind (Regensburg)

Abstract: T-duality arose in string theory as an equivalence between the physics of two different but suitable related spacetimes. By considering only the underlying topological quantities, T-duality can be distilled into a mathematical theorem which states that the twisted K-theories of certain pairs of circle bundles equipped with U(1)-gerbes are isomorphic via a Fourier-Mukai transform. In this talk, I will describe a generalization of T-duality to higher rank sphere bundles. I will construct twists of the iterated algebraic K-theory of connective complex K-theory by higher gerbes and describe a T-duality isomorphism between the twisted iterated K-theories of a pair of suitably related sphere bundles. (Joint with H. Sati and C. Westerland)

4:00 pm in 245 Altgeld Hall,Thursday, February 18, 2016

#### New Interactions between Analysis and Number Theory

###### Stefan Steinerberger (Yale)

Abstract: I will tell three unrelated stories describing new mysteries occurring somewhere inbetween Analysis and Number Theory. (1) The Poincare inequality is a cornerstone of mathematical physics (and related to the behavior of vibrating membranes/plates). I will present a curious improvement on the Torus that has a strong number theoretical flavor - even Fibonacci numbers appear. (2) If the Hardy-Littlewood maximal function of f(x) is “easy" to compute, then f(x)=sin(x). This weird definition of sin(x) has applications in delay-differential equations. One would think that any characterization of sin(x) would be straightforward to prove, and yet the only proof I could find of this one relies on a fantastic miracle to occur (and transcendental number theory). (3) An old integer sequence (1,2,3,4,6,8...) defined by Stanislaw Ulam in the 1960s turns out to have very strange properties, giving rise to surprising pictures.