Date/Time : 19 Mar 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Edmund Karasiewicz, National University of Singapore

In this mini course we will study two topics. The first is the PGL2xF4 exceptional theta correspondence over a p-adic field. The second is the dual group of a spherical variety. Over the course of four lectures we will:

1. Introduce exceptional groups, focusing on constructions and tools relevant to the exceptional theta correspondence.
2. Describe the PGL2xF4 exceptional theta correspondence over a p-adic field.
3. Present the combinatorial construction of the dual group of a spherical variety due to Knop-Schalke.
4. Connect the exceptional theta correspondence to the F4/Spin9 spherical variety.

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https://nus-sg.zoom.us/j/84884850855?pwd=bvokLMShAf5wFeAHh2zemmel1dvb9f.1

Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 04 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Xie Kaitao, The University of Hong Kong

The totally nonnegative part of flag varieties has been studied extensively for many years, and many remarkable properties have been established. Motivated by the study of higher Teichmuller theory, Guichard and Wienhard generalized Lusztig’s notion of total positivity and introduce theta positivity. In this talk, I will discuss the analogues for a family of theta nonnegative part of Lagrangian Grassmannian.

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Date/Time : 04 Mar 2025 15:00
Venue : S17 #05-11 (SR5)
Speaker : Max Gurevich, Technion - Israel Institute of Technology

For a split reductive p-adic group G, one can choose a hyperspecial maximal compact subgroup K and its Iwahori subgroup I. The resulting Hecke algebra H(I\K/I) is on one hand understood as a deformation of the Weyl group W of G; on the other, it acts on representations in the principal Bernstein block of G-representations.

With the p-adic story set aside, the geometric theory of Weyl group representations is expressed in the Springer correspondence, which parametrizes the spectrum of W in terms of local systems on unipotent conjugacy classes of the complex Langlands dual group to G.

When G is of classical type, the same local systems also arise as parameters in Arthur’s endoscopic approach to Langlands reciprocity. With Emile Okada, we explore the interplay between these two sets of parameters attached to irreducible representations, investigating their compatibility with natural restriction functors.

If time permits, I will explain one angle of broader motivation: an expectation relating local Arthur packets to the notion of ‘weak sphericity’ of representations. Interestingly, this property is most naturally analyzed through its specialization to the domain of Weyl group representations.

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Date/Time : 26 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 : 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

Add to calendar :

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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