Date/Time : 16 Apr 2025 9:30
Venue : S17 #05-11 (SR5)
Speaker : Jishnu Kundu, National University of Singapore

The Relative Trace formula is a generalization of the Arthur Selberg trace formula and has its role in better understanding the automorphic representations of a general reductive group G. The talk will concern about the terms contributing to the spectral and geometric sides of the formula and concluded by a number theoretic application of it.

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Date/Time : 16 Apr 2025 10:20
Venue : S17 #05-11 (SR5)
Speaker : Leong Jin Ming, National University of Singapore

One of the main “conjectures” in the Relative Langlands Duality program launched by Ben-Zvi, Sakellaridis and Venkatesh is a duality between anomaly free hyperspherical pairs. In this talk we will explore the concept of anomaly freeness and use an equivalent representation theoretic formulation to work out which pairs are anomaly free.

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Date/Time : 15 Apr 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Yotsanan Meemark, Chulalongkorn University

For a finite ring R with identity the unitary Cayley graph of R, C_R, is the graph with vertex set R and for each x, y in R, x and y are adjacent if and only if x-y is a unit of R. In this talk we will discuss many results on the structure parameters (e.g., clique number, chromatic number) and eigenvalues of this graph. We analyze the energy (the sum of eigenvalues) and characterize the ring R such that C_R is Ramanujan. Our combinatorial number-theoretic approaches mainly come from properties of finite rings and fields and their characters.

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Date/Time : 09 Apr 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 : 08 Apr 2025 14:50
Venue : S17 #05-11 (SR5)
Speaker : Guodong Tang, National University of Singapore

The recent joint work of Ben-Zvi, Sakellaridis and Venkatesh (BZSV) proposed a duality of the relative Langlands problem though the concept of hyperspherical data (G, H, \iota, S). A natural question under this framework is the classification of such spaces and their duals. This talk, based on Joven’s presentation on nilpotent orbits, I will explain the follow-up work of Gan and Wang for the case where G = SO_{2n+1}, Sp_{2n}, and SO_{2n}, as well as the joint work of Zhang, Wan, and myself on the exceptional case on exceptional case though G = F_4.

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Date/Time : 08 Apr 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Joven Teo, National University of Singapore

In this introductory talk, we give a basic overview of nilpotent orbits and how they show up in the context of the relative Langlands duality proposed by Ben-Zvi, Sakellaridis, and Venkatesh. We then illustrate some of these concepts by looking at a specific example in detail.

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Date/Time : 02 Apr 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 : 01 Apr 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Li Anlun, National University of Singapore

In the study of the spherical variety X=H\G, it’s crucial to study the period integral P_H of some (cuspidal) automorphic forms of G. In this talk we will study the case G=G_2 and H=SL_3. Under assumptions about the dimension 1 condition of some Hom spaces, we can show that the global period integral can be related to the local H-invariant linear functional that comes from the Plancherel theorem of Mp_2 and the theta correspondence from Mp_2 to G_2. Moreover, since this Hom space is (assumed to be) 1 dimensional, we can determine the coefficient by showing an analogue of the Siegel-Weil formula.

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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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