Date/Time : 01 Apr 2025 14:50
Venue : S17 #05-11 (SR5)
Speaker : Colin Loh, National University of Singapore

Recent work of Mao, Wan and Zhang have provided a complete list of strongly tempered hyperspherical varieties and they proposed some new Rankin-Selberg integrals. In this talk, I will present 3 new Rankin-Selberg integrals associated to dual of strongly tempered distinguished polarised hyperspherical varieties and discuss the L-functions these integrals represent, as examples of the Relative Langlands Duality.

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Date/Time : 27 Mar 2025 16:00
Venue : S17 #06-11 (SR6)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

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Date/Time : 26 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.

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

Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 26 Mar 2025 14:00
Venue : S17 #06-11 (SR6)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

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Date/Time : 25 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

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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.

Join Zoom Meeting
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

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