Calendar

Posted October 6, 2025
Last modified October 13, 2025

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Paul Kirk, Indiana University
On the SU(2) character variety of a closed oriented genus 2 surface

A celebrated theorem of Narasimhan-Ramanan asserts that the singular variety $X(F_2)=Hom(\pi_1(F_2),SU(2))/Conjugation$ is homeomorphic to $CP^3$. The proof passes through the (mysterious) Narasimhan-Seshadri correspondence. I'll outline an elementary differential topology proof that $X(F_2)$ is a manifold, homeomorphic to CP^3, and discuss how 3-manifolds with genus 2 boundary determine embedded lagrangians in $X(F_2)$. If time permits, I'll end the talk with a discussion of context, particularly with a program known as the Atiyah-Floer conjecture.

Posted October 21, 2025

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Michael Lacey, Georgia Institute of Technology
Prime Wiener Wintner Theorem

The classical Wiener Wintner Theorem has an extension to prime averages. Namely, for all measure preserving system $(X,m,T)$, and bounded function $f$ on $X$, there is a set of full measure $X_f\subset X$ so that for all $x\in X_f$, the averages below $$ \frac 1N \sum_{n=1}^N \phi(n) \Lambda (n) f(T^n x ) $$ converge for all continuous $2\pi$ periodic $\phi $. Above, $\Lambda$ is the von Mangoldt function. The proof uses the structure theory of measure preserving systems, the Prime Ergodic Theorem, and higher order Fourier properties of the Heath-Brown approximate to the von Mangoldt function. Joint work with J. Fordal, A. Fragkos, Ben Krause, Hamed Mousavi, and Yuchen Sun.

Posted August 19, 2025

Colloquium Questions or comments?

David Roberts, University of Minnesota, Morris
TBA