seminars:colloquium
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seminars:colloquium [2024/02/26 12:16] malkiewich Klein TA |
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| ====== Colloquium ====== | ====== Colloquium ====== | ||
| - | Unless stated otherwise, colloquia are scheduled for Thursdays 4:15-5:15pm in WH-100E with refreshments served from 4:00-4:15 pm in WH-102. | + | Unless stated otherwise, colloquia are scheduled for Thursdays 4:00-5:00pm in WH-100E with refreshments served from 3:45-4:00 pm in WH-102. |
| - | Organizers: [[people:kargin:start|Vladislav Kargin]], [[people:malkiewich:start]], [[people:tongviet:start]], | + | Organizers: [[people:dobbins:start]], [[people:kargin:start|Vladislav Kargin]], [[people:malkiewich:start]], |
| - | and [[people:adrian:start]] | + | [[people:adrian:start]], and [[people:ewyman:start]] |
| ----- | ----- | ||
| - | ==== Spring 2024 ==== | + | ==== Fall 2025 ==== |
| - | **Thursday Feb 29 4:15-5:15pm, WH-100E**\\ //Speaker//: ** [[ https://people.math.rochester.edu/faculty/iosevich/ | Alex Iosevich]] ** (University of Rochester) \\ //Topic//: **//Signal recovery, uncertainty principles and Fourier restriction theory//** \\ | + | **Thursday Nov 6 4:00-5:00pm, WH-100E**\\ //Speaker//: ** [[ https://blogs.baruch.cuny.edu/aobus/ | Andrew Obus]] ** (CUNY) \\ //Topic//: **//The lifting problem for covers of curves, particularly its group-theoretical aspects//** \\ |
| <WRAP box 90%> | <WRAP box 90%> | ||
| **//Abstract//**: | **//Abstract//**: | ||
| - | We are going to consider functions $f: {\mathbb Z}_N \to {\mathbb C}$ and view them as signals. Suppose that we transmit this signal via its Fourier transform | + | Whenever a mathematical object is given in |
| - | $$\widehat{f}(m)=\frac{1}{N} \sum_{x=0}^{N-1} e^{-\frac{2 \pi i xm}{N}} f(x),$$ | + | characteristic p, one can ask whether it is the reduction, in some |
| + | sense, of an analogous structure in characteristic zero. If so, the | ||
| + | structure in characteristic zero is called a "lift" of the structure | ||
| + | in characteristic p. The most famous example is Hensel's Lemma about | ||
| + | lifting solutions of polynomials in Z/p to solutions in the p-adic | ||
| + | integers Z_p. | ||
| - | and that the values of $\widehat{f}(m), m \in S$, are lost. Under what circumstances is it possible to recover the original signal? We shall see how this innocent question quickly leads us into the deep dark forest of Fourier analysis.\\ | + | The “lifting problem” we consider is more geometric: given a smooth curve X in |
| + | characteristic p with an action of a finite group G, is there a curve | ||
| + | in characteristic zero with G-action that reduces to X? Unsurprisingly, the answer is related to the group theory of G (for instance, if p does not divide |G| or if G is cyclic, then the curve with the G-action always lifts, but if G has an abelian, non-cyclic, non-p-subgroup that fixes a point on X, then the curve does not lift with the action). After giving an introduction to the lifting problem and some examples, we will discuss well-established ways that the problem interacts with group theory, as well as more recent advances relating the problem to representation theory.\\ | ||
| </WRAP> | </WRAP> | ||
| - | **Thursday March 14 4:15-5:15pm, WH-100E**\\ //Speaker//: ** [[ https://klein.wayne.edu/ | John Klein]] ** (Wayne State University) \\ //Topic//: **//On a rationality problem in quantum information theory//** \\ | ||
| - | <WRAP box 90%> | ||
| - | **//Abstract//**: | ||
| - | In this talk, I shall consider the case of quantum systems consisting of n parties, in which each party is in possession of a qubit, i.e., | ||
| - | a two dimensional complex vector space. Each qubit is allowed to evolve independently, and the group G of local symmetries governs the evolution of the n-qubit system. | ||
| - | My goal will be to provide a complete description of the field G-invariant complex valued functions on the space of mixed states of this quantum system. | ||
| - | Such functions are to be viewed as detailed measures of entanglement. | ||
| - | \\ | ||
| - | </WRAP> | ||
| - | **[[hiltonmemorial:lecture2024|PETER HILTON MEMORIAL LECTURE]]**\\ | ||
| - | **Thursday April 11th 3:00pm-4:00pm, LH-009**\\ //Speaker//: ** [[ https://www.math.uchicago.edu/~eskin/ |Alex Eskin]] ** (University of Chicago) \\ //Topic//: **//Polygonal Billiards and Dynamics on Moduli Spaces//** \\ | ||
| - | <WRAP box 90%> | ||
| - | **//Abstract//**: | ||
| - | Billiards in polygons can exhibit bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry, Teichmuller theory and ergodic theory on homogeneous spaces. The talk will be an introduction to these ideas, aimed at a general mathematical audience.\\ | ||
| - | </WRAP> | ||
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| * [[seminars:colloquium:y2021-2022|2021-2022]] | * [[seminars:colloquium:y2021-2022|2021-2022]] | ||
| * [[seminars:colloquium:y2022-2023|2022-2023]] | * [[seminars:colloquium:y2022-2023|2022-2023]] | ||
| + | * [[seminars:colloquium:y2023-2024|2023-2024]] | ||
seminars/colloquium.1708967760.txt · Last modified: 2025/09/04 15:00 (external edit)