Colloquia: Difference between revisions
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Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients. | Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients. | ||
'''Friday, September 22. David Dumas''' | |||
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research. | |||
'''Friday, October 13. Autumn Kent''' | '''Friday, October 13. Autumn Kent''' | ||
Revision as of 18:18, 15 September 2023
UW Madison mathematics Colloquium is on Fridays at 4:00 pm unless otherwise noted.
Fall 2023
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| Sept 8 | Tushar Das (University of Wisconsin-La Crosse) | Playing games on fractals: Dynamical & Diophantine | Stovall | |
| Sept 15 | John Schotland (Yale) | Nonlocal PDEs and Quantum Optics | Li | |
| Sept 22 | David Dumas(University of Illinois Chicago) | Geometry of surface group homomorphisms | Zimmer | |
| Sept 29 | ||||
| Monday Oct 2 at 4 pm | Edriss Titi (Texas A&M University) | Distinguished lectures | Smith, Stechmann | |
| Oct 13 | Autumn Kent | The 0π Theorem | ||
| Oct 20 | Sara Maloni (UVA) | Dymarz, Uyanik, GmMaW | ||
| Wednesday Oct 25 at 4 pm | Gigliola Staffilani (MIT) | Ifrim, Smith | ||
| Oct 27 | Rodrigo Bañuelos (Purdue) | Stovall | ||
| Tuesday Oct 31 at 4 pm | Irit Dinur (The Weizmann Institute of Science) | Distinguished lectures | Gurevich | |
| Wednesday Nov 1 at 4 pm | Irit Dinur (The Weizmann Institute of Science) | Distinguished lectures | Gurevich |
Abstracts
Friday, September 8. Tushar Das
Playing games on fractals: Dynamical & Diophantine We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.
Friday, September 15. John Schotland
Nonlocal PDEs and Quantum Optics Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.
Friday, September 22. David Dumas
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.
Friday, October 13. Autumn Kent
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.