Colloquia/Fall2025: Difference between revisions
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! align="left" | title | ! align="left" | title | ||
! align="left" | host(s) | ! align="left" | host(s) | ||
|- | |- | ||
|October 3, 2025 | |October 3, 2025 | ||
|Hong Wang (NYU and IHES) | |Hong Wang (NYU and IHES) | ||
| | |Restriction theory and projection theorems | ||
|Seeger, Stovall, Street | |Seeger, Stovall, Street | ||
|- | |- | ||
|Monday, October 6, 4 pm in VV B239 | |Monday, October 6, 4 pm in VV B239 | ||
|Wei Zhang (Distinguished Lectures) (MIT) | |Wei Zhang (Distinguished Lectures) (MIT) | ||
| | |Gross-Zagier formula in high dimensions, I | ||
|Yang | |Yang | ||
|- | |- | ||
|Tuesday, October 7, 4 pm in VV B239 | |Tuesday, October 7, 4 pm in VV B239 | ||
|Wei Zhang (Distinguished Lectures) (MIT) | |Wei Zhang (Distinguished Lectures) (MIT) | ||
| | |Gross-Zagier formula in high dimensions, II | ||
| | | | ||
| | | | ||
|- | |- | ||
|Wednesday, October 8, 12 pm in | |Wednesday, October 8, 12 pm in Birge 302 | ||
|Wei Zhang (Distinguished Lectures) (MIT) | |Wei Zhang (Distinguished Lectures) (MIT) | ||
| | |Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas | ||
| | | | ||
| | | | ||
| Line 40: | Line 35: | ||
|October 10, 2025 | |October 10, 2025 | ||
|Joseph Maher (CUNY) | |Joseph Maher (CUNY) | ||
| | |Generic elements in mapping class groups | ||
|Uyanik | |Uyanik | ||
|- | |- | ||
| Line 48: | Line 43: | ||
|Gurevich | |Gurevich | ||
|- | |- | ||
|''' | |'''Wednesday,''' 4 pm, October 22, 2025, VV B239 | ||
|Aaron Naber (Distinguished Lectures) (IAS) | |Aaron Naber (Distinguished Lectures) (IAS) | ||
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|October | |'''Thursday,''' 4 pm, October 23, 2025, Ingraham 0022 | ||
|Aaron Naber (Distinguished Lectures) (IAS) | |Aaron Naber (Distinguished Lectures) (IAS) | ||
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| Line 72: | Line 67: | ||
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|- | |- | ||
|'''Wednesday''', | |'''Wednesday,''' '''4 pm''', November 12, 2025 | ||
|Rachel Greenfeld (Northwestern) | |Rachel Greenfeld (Northwestern) | ||
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== '''Abstracts''' == | |||
=== October 3: Hong Wang (NYU and IHES) === | |||
Title: Restriction theory and projection theorems | |||
Abstract: Restriction theory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation). Projection theorems study the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions. | |||
=== October 6: Wei Zhang (MIT) === | |||
'''Lectures 1 and 2: Monday (Oct. 6) and Tuesday (Oct. 7) 4-5pm, VV B239''' | |||
Title: Gross-Zagier formula in high dimensions (I, II) | |||
Abstract: In their 1986 paper, Gross and Zagier proved a formula relating a special rational point on an elliptic curve to the first derivative of the L-function associated with that curve. The Gross–Zagier formula, together with Kolyvagin’s Euler system, yielded a major advance toward the Birch–Swinnerton-Dyer conjecture for elliptic curves. Since then, generalizing this fundamental result to higher-dimensional algebraic varieties has become a central area of interest. In this talk, I will present some of these generalizations, focusing on relatively recent developments, with particular emphasis on Kudla’s program and the arithmetic Gan–Gross–Prasad conjecture. Much like the Gross–Zagier formula, these generalizations have found important applications to the Beilinson–Bloch–Kato conjecture, which extends the Birch–Swinnerton-Dyer conjecture to higher-dimensional varieties. | |||
'''Lecture 3: Wednesday, Oct. 8, 12-1pm. Birge B302''' | |||
Title: Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas | |||
Abstract: The volume of a locally symmetric space can be expressed essentially as a product of special values of zeta functions. More generally, Hirzebruch’s proportionality theorem, later extended by Mumford, describes how to integrate any Chern class polynomial on a locally symmetric space. A natural next step is to study the arithmetic volumes of Shimura varieties, as well as their analogues for the moduli spaces of Drinfeld Shtukas over function fields. In this talk, we will report on joint work in progress with Tony Feng and Zhiwei Yun addressing this question. | |||
=== October 10: Joseph Maher(CUNY)=== | |||
Title: Generic elements in mapping class groups | |||
Abstract: We will give an introduction to various approaches of defining | |||
generic elements in groups, paying particular attention to random walks, | |||
and groups with various coarse negative curvature properties, including | |||
the mapping class groups of surfaces. As time permits, we will discuss | |||
some recent joint work with Jing Tao, showing that the elements obtained | |||
from Thurston's filling multicurve construction are not generic in the | |||
mapping class group. | |||
Latest revision as of 02:40, 26 September 2025
UW-Madison Mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.
mathcolloquium@g-groups.wisc.edu is the mailing list. Everyone in the math department is subscribed.
The main contact is Dallas Albritton. Secondary contact is Paul Apisa.
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| October 3, 2025 | Hong Wang (NYU and IHES) | Restriction theory and projection theorems | Seeger, Stovall, Street | |
| Monday, October 6, 4 pm in VV B239 | Wei Zhang (Distinguished Lectures) (MIT) | Gross-Zagier formula in high dimensions, I | Yang | |
| Tuesday, October 7, 4 pm in VV B239 | Wei Zhang (Distinguished Lectures) (MIT) | Gross-Zagier formula in high dimensions, II | ||
| Wednesday, October 8, 12 pm in Birge 302 | Wei Zhang (Distinguished Lectures) (MIT) | Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas | ||
| October 10, 2025 | Joseph Maher (CUNY) | Generic elements in mapping class groups | Uyanik | |
| October 17, 2025 | Vadim Gorin (UC Berkeley) | Gurevich | ||
| Wednesday, 4 pm, October 22, 2025, VV B239 | Aaron Naber (Distinguished Lectures) (IAS) | Waldron | ||
| Thursday, 4 pm, October 23, 2025, Ingraham 0022 | Aaron Naber (Distinguished Lectures) (IAS) | Waldron | ||
| October 31, 2025 | Henri Berestycki (Maryland/EHESS) | Graham | ||
| November 7, 2025 | ||||
| Wednesday, 4 pm, November 12, 2025 | Rachel Greenfeld (Northwestern) | Seeger, Stovall | ||
| November 21, 2025 | Reserved | Smith | ||
| November 28, 2025 | Thanksgiving Week (No Colloquium) | |||
| December 5, 2025 | Reserved | Smith |
Abstracts
October 3: Hong Wang (NYU and IHES)
Title: Restriction theory and projection theorems
Abstract: Restriction theory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation). Projection theorems study the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions.
October 6: Wei Zhang (MIT)
Lectures 1 and 2: Monday (Oct. 6) and Tuesday (Oct. 7) 4-5pm, VV B239
Title: Gross-Zagier formula in high dimensions (I, II)
Abstract: In their 1986 paper, Gross and Zagier proved a formula relating a special rational point on an elliptic curve to the first derivative of the L-function associated with that curve. The Gross–Zagier formula, together with Kolyvagin’s Euler system, yielded a major advance toward the Birch–Swinnerton-Dyer conjecture for elliptic curves. Since then, generalizing this fundamental result to higher-dimensional algebraic varieties has become a central area of interest. In this talk, I will present some of these generalizations, focusing on relatively recent developments, with particular emphasis on Kudla’s program and the arithmetic Gan–Gross–Prasad conjecture. Much like the Gross–Zagier formula, these generalizations have found important applications to the Beilinson–Bloch–Kato conjecture, which extends the Birch–Swinnerton-Dyer conjecture to higher-dimensional varieties.
Lecture 3: Wednesday, Oct. 8, 12-1pm. Birge B302
Title: Proportionality and the arithmetic volumes of Shimura varieties and the moduli of Shtukas
Abstract: The volume of a locally symmetric space can be expressed essentially as a product of special values of zeta functions. More generally, Hirzebruch’s proportionality theorem, later extended by Mumford, describes how to integrate any Chern class polynomial on a locally symmetric space. A natural next step is to study the arithmetic volumes of Shimura varieties, as well as their analogues for the moduli spaces of Drinfeld Shtukas over function fields. In this talk, we will report on joint work in progress with Tony Feng and Zhiwei Yun addressing this question.
October 10: Joseph Maher(CUNY)
Title: Generic elements in mapping class groups
Abstract: We will give an introduction to various approaches of defining generic elements in groups, paying particular attention to random walks, and groups with various coarse negative curvature properties, including the mapping class groups of surfaces. As time permits, we will discuss some recent joint work with Jing Tao, showing that the elements obtained from Thurston's filling multicurve construction are not generic in the mapping class group.