Date/Time : 19 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 12 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

Add to calendar :

Date/Time : 11 Feb 2025 16:00
Venue : S17 #05-11 (SR5)
Speaker : Travis Scrimshaw, Hokkaido University

Key polynomials originally arose as characters of natural representations of upper triangular matrices coming from Schubert calculus. They have many algebraic properties similar to Schur functions, such as a Cauchy-type formula and form a basis for the polynomial ring. For this talk, we consider them to be special polynomials that are defined recursively by divided difference operators. We recall the Bump-Brubaker-Buciumas-Gustafsson construction using colored solvable lattice models to transform this into a combinatorial interpretation using semistandard tableaux. Using Kashiwara’s theory of crystal base, we recall another way to interpret the tableaux. We will conclude the talk with some recent generalizations of these constructions and open questions. This is based on joint work with Valentin Buciumas and Katherine Weber and with Eric Marberg.

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Date/Time : 11 Feb 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Christian Johansson, University of Gothenburg

I will discussion joint work with James Newton and Carl Wang-Erickson, where we give an interpretation of the p-adic local Langlands correspondence for GL(2,Qp) as an embedding of the derived category of locally admissible representation into the category of ind-coherent sheaves on the moduli stack of Galois representations. Time permitting, I will also discuss local-global formulas.

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Date/Time : 04 Feb 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : David Hansen, National University of Singapore

The Bernstein center of a p-adic reductive group G is a beautiful and explicit commutative ring which acts on “everything” related to the representation theory of G. In recent years, the idea has emerged that this ring contains a canonical subring – the stable Bernstein center – which should be intimately related with the local Langlands correspondence. However, while it is easy to define the stable Bernstein center, it is very difficult to exhibit elements in this subring. On the other hand, recent work of Fargues-Scholze defines another totally canonical subring of the Bernstein center, whose construction uses V. Lafforgue’s theory of excursion operators adapted to the Fargues-Fontaine curve. After reviewing these stories, I’ll sketch a proof that the Fargues-Scholze subring is actually contained in the stable Bernstein center, for all G.

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Date/Time : 22 Jan 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:
1. Models of the Heisenberg-Weil representation and the Metaplectic group 2. Dual pairs and general properties of theta correspondences 3. Theta correspondences over real fields 4. Theta correspondences over finite fields and p-adic fields 5. Geometric aspects of theta correspondence This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 21 Jan 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Hui Gao, Southern University of Science and Technology

Using the Breuil–Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.

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Date/Time : 15 Jan 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course focuses on the fundamental aspects of local theta correspondence. In the first lecture, we will examine the Weil representation in detail. We will explore various realizations of the Weil representation and definitions of the Metaplectic group. Additionally, we will discuss the definition of the Weil index and related concepts. The course material is based on Gan-Kudla-Takada’s book The Local Theta Correspondence. This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream.  Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 07 Jan 2025 16:00
Venue : S17 #05-12 (SR4)
Speaker : Chen Wan, Rutgers University—Newark

In this talk, I will discuss the geometric expansion of a local (twisted) trace formula for some special varieties. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur and Waldspurger. By applying the trace formula, we prove a multiplicity formula for these spherical varieties. And I will also discuss some applications to the multiplicity of the Galois model and the unitary Shalika model. This is a joint work with Raphael Beuzart-Plessis.

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