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일정시작 2022-03-25
일정종료 2022-03-25
배경색상 #036eb7
  • 2022년 3월 QSMS  Monthly Seminar
  • Date:   25 March  Fri  PM 2:00 ~ 5:00
  • Place:  129-101 (SNU)

 

  • Speaker:  유화종 Hwajong Yoo (PM 2:00 ~ 3:00)
  • Title:  The dimension of the kernel of an Eisenstein ideal
  • Abstract:  We introduce a notion of multiplicity one for modular Jacobian varieties, which is about the dimension of the kernel of a certain maximal ideal of the Hecke algebra. When such a maximal ideal is non-Eisenstein (which will be explained), then multiplicity one holds (which means that the dimension is 2.) On the other hand, as first noticed by Calegari and Stein, multiplicity one often fails for Eisenstein maximal ideals. We propose a conjecture about the dimension of the kernel of an Eisenstein ideal. If time permits, we sketch the proof of my work with Ken Ribet.

 

  • Speaker:  조창연 Chang-Yeon Chough (PM 4:00 ~ 5:00) 
  • TiTle:   Twisted equivalences in spectral algebraic geometry
  • Abstract:   Derived equivalence has been an interesting subject in relation to Fourier-Mukai transform, Hochschild homology, and algebraic K-theory, just to name a few. On the other hand, the attempt to classify schemes by their derived categories twisted by elements of Brauer groups is very restrictive as we have a positive answer only for affines. I'll talk about how we can extend this result to a broader class of algebro-geometric objects in the setting of derived/spectral algebraic geometry at the expense of a stronger notion of twisted equivalences than that of ordinary twisted derived equivalences. I'll convince you that the new notion is not only reasonable but also indispensable from this point of view. The first half will be mainly devoted to giving brief expository accounts of some background materials needed to understand the notion of twisted derived equivalence in the setting of derived/spectral algebraic geometry. The remaining half will cover a derived/spectral analog of Rickard's theorem, which shows that derived equivalent associative rings have isomorphic centers. I'll try to avoid technicalities related to using the language of derived/spectral algebraic geometry.

     

 

 

 

 

 


List of Articles
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134 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 1494
133 [QSMS Monthly Seminar 2022-09-30] Monotone Lagrangians via toric degenerations: algebraic approach qsms 2022.09.30 1358
132 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 1244
131 [QSMS Monthly Seminar 2022-12-02] Extended crystal structures of Hernandez-Leclerc categories qsms 2022.12.02 1275
130 [QSMS Monthly Seminar 2023-03-24] Rational points on abelian varieties qsms 2023.03.24 1176
129 [QSMS Monthly Seminar 2023-04-21] Lagrangian submanifolds and their Legendrian lifts qsms 2023.04.21 1151
128 [QSMS Monthly Seminar 2023-05-26] Lagrangian submanifolds and their Legendrian lifts qsms 2023.05.26 1136
127 [QSMS Monthly Seminar 2023-10-13] Quantum Grothendieck rings of Hernandez-Leclerc categories / Regular Schur labeled skew shape posets and their 0-Hecke modules qsms 2023.10.13 979
126 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 1073
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