Date/Time : 18 Sep 2019 10:00
Venue : S16 #03-09
Speaker : Bao Huanchen, National University of Singapore

Date/Time:18 Sep 2019 10:00 Venue: S16 #03-09 Speaker: Bao Huanchen, National University of Singapore Total positivity in reductive groups II I will explain the cellular decompositions of totally nonnegative flag variety and totally nonnegative springer fibres. The references are the following: K. Rietsch, “An algebraic cell decomposition of the nonnegative part of a flag variety”; R. Marsh and K. Rietsch, “Parametrizations of flag varieties’’; G. Lusztig, “Total positivity in Springer fibres”. Add to calendar: 

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Date/Time : 11 Sep 2019 10:00
Venue : S16 #03-09
Speaker : Bao Huanchen, National University of Singapore

Date/Time:11 Sep 2019 10:00 Venue: S16 #03-09 Speaker: Bao Huanchen, National University of Singapore Total positivity in reductive groups I will explain Lusztig’s theory of total positivity. I shall follow (mainly) his 1994 paper of the same title. Add to calendar: 

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Date/Time : 04 Sep 2019 10:00
Venue : S16 #03-09
Speaker : Cheng Yao, Sinica

Date/Time:04 Sep 2019 10:00 Venue: S16 #03-09 Speaker: Cheng Yao, Sinica Special Value formula for twisted triple product L-function and an application to the restricted L^2-norm problem In this talk we will present an explicit Ichino’s formula [Ich08] for the central value of the twisted triple product L-function associated to Maass forms. To establish such a formula one need to carry out explicit computations for the local period integrals appearing in Ichino’s formula. We prove an identity between the local period integral and a product of two Rankin-Selberg integrals in order to simplify the calculations. This identity generalizes the result in [MV10]. Our explicit formula has an application to the optimal upper bound of a sum of restricted L^2-norms of the L^2-normalized newforms on certain quadratic extensions with prime level and bounded spectral parameter. For this we follow the methods in [Blo13]. References: [Blo13] Valentin Blomer. On the 4-norm of an automorphic form. Journal of European Mathematical Society, 15:1825–1852, 2013. [Ich08] A. Ichino. Trilinear forms and the central values of triple product L-functions. Duke Mathematical Journal, 145(2):281– 307, 2008. [MV10] P. Michel and A. Venkatesh. The subconvexity problem for GL2. Publ. Math. Inst. Hautes Etudes Sci., (111):171–271, 2010. Add to calendar: 

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