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'''Friday, September 8. Tushar Das''' | '''Friday, September 8. Tushar Das''' | ||
Playing games on fractals: Dynamical & Diophantine | 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. | 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. | ||
==Future Colloquia== | ==Future Colloquia== | ||
Revision as of 14:59, 5 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) | Li | ||
| Sept 22 | David Dumas | Zimmer | ||
| Sept 29 | Kaie Kubjas (Aalto University) | The geometry of 3D genome reconstruction | Rodriguez | |
| 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
Template:Anchor:tushardas 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.