Colloquia/Spring2019: Difference between revisions
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| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) | | [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) | ||
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== Abstracts == | == Abstracts == | ||
===Lillian Pierce (Duke University)=== | |||
Title: Short character sums | |||
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations. | |||
===Aaron Naber (Northwestern)=== | ===Aaron Naber (Northwestern)=== | ||
Revision as of 22:15, 21 January 2019
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Spring 2019
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| Jan 25 | Beata Randrianantoanina (Miami University Ohio) WIMAW | TBA | Tullia Dymarz | |
| Jan 30 Wednesday | Lillian Pierce (Duke University) | Short character sums | Boston and Street | |
| Jan 31 Thursday | Dean Baskin ( Texas A&M) | TBA | Street | |
| Feb 1 | Jianfeng Lu (Duke University) | TBA | Qin | |
| Feb 5 Tuesday | Alexei Poltoratski (Texas A&M University) | TBA | Denisov | |
| Feb 8 | Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds | Street | |
| Feb 15 | TBA | |||
| Feb 22 | Angelica Cueto (Ohio State) | TBA | Erman and Corey | |
| March 4 | Vladimir Sverak (Minnesota) Wasow lecture | TBA | Kim | |
| March 8 | Jason McCullough (Iowa State) | TBA | Erman | |
| March 15 | Maksym Radziwill (Caltech) | TBA | Marshall | |
| March 29 | Jennifer Park (OSU) | TBA | Marshall | |
| April 5 | Ju-Lee Kim (MIT) | TBA | Gurevich | |
| April 12 | Evitar Procaccia (TAMU) | TBA | Gurevich | |
| April 19 | Jo Nelson (Rice University) | TBA | Jean-Luc | |
| April 26 | Kavita Ramanan (Brown University) | TBA | WIMAW | |
| May 3 | Tomasz Przebinda (Oklahoma) | TBA | Gurevich |
Abstracts
Lillian Pierce (Duke University)
Title: Short character sums
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.
Aaron Naber (Northwestern)
Title: A structure theory for spaces with lower Ricci curvature bounds.
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.
<DATE>: <PERSON> (INSTITUTION)
Title: <TITLE>
Abstract: <ABSTRACT>