Wednesday, August 19, 2020

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2020-08-25 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: Extremal problems and probabilistic methods in hyperbolic geometry 인쇄
by (Institut de Mathématiques de Jussieu-Paris Rive Ga)
(Continued) Even if we know many things about hyperbolic manifolds, there are many open extremal problems on them. To name a few: - How does the maximal systole among closed hyperbolic n-manifolds of volume at most V grow as a function of V? - How does the minimal diameter among closed hyperbolic n-manifolds of volume at least V grow as a function of V? - Are there closed hyperbolic n-manifolds of arbitrarily large volume whose spectral gap is larger than that of hyperbolic n-space? Even for surfaces (i.e n=2), many of these extremal problems are open. In this case, answers to these questions also provide insight into the shape of deformation spaces of hyperbolic surfaces. In these lectures, I will discuss some of these problems. I will talk about what is known about them and how random constructions of hyperbolic manifolds sometimes provide answers.
2020-08-24 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: Extremal problems and probabilistic methods in hyperbolic geometry 인쇄
by Bram Petri(Institut de Mathématiques de Jussieu-Paris Rive Ga)
(Continued) Even if we know many things about hyperbolic manifolds, there are many open extremal problems on them. To name a few: - How does the maximal systole among closed hyperbolic n-manifolds of volume at most V grow as a function of V? - How does the minimal diameter among closed hyperbolic n-manifolds of volume at least V grow as a function of V? - Are there closed hyperbolic n-manifolds of arbitrarily large volume whose spectral gap is larger than that of hyperbolic n-space? Even for surfaces (i.e n=2), many of these extremal problems are open. In this case, answers to these questions also provide insight into the shape of deformation spaces of hyperbolic surfaces. In these lectures, I will discuss some of these problems. I will talk about what is known about them and how random constructions of hyperbolic manifolds sometimes provide answers.
2020-08-21 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: Extremal problems and probabilistic methods in hyperbolic geometry 인쇄
by Bram Petri(Institut de Mathématiques de Jussieu-Paris Rive Ga)
(Continued) Even if we know many things about hyperbolic manifolds, there are many open extremal problems on them. To name a few: - How does the maximal systole among closed hyperbolic n-manifolds of volume at most V grow as a function of V? - How does the minimal diameter among closed hyperbolic n-manifolds of volume at least V grow as a function of V? - Are there closed hyperbolic n-manifolds of arbitrarily large volume whose spectral gap is larger than that of hyperbolic n-space? Even for surfaces (i.e n=2), many of these extremal problems are open. In this case, answers to these questions also provide insight into the shape of deformation spaces of hyperbolic surfaces. In these lectures, I will discuss some of these problems. I will talk about what is known about them and how random constructions of hyperbolic manifolds sometimes provide answers.
2020-08-19 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: Extremal problems and probabilistic methods in hyperbolic geometry 인쇄
by Bram Petri(Institut de Mathématiques de Jussieu-Paris Rive Ga)
Even if we know many things about hyperbolic manifolds, there are many open extremal problems on them. To name a few: - How does the maximal systole among closed hyperbolic n-manifolds of volume at most V grow as a function of V? - How does the minimal diameter among closed hyperbolic n-manifolds of volume at least V grow as a function of V? - Are there closed hyperbolic n-manifolds of arbitrarily large volume whose spectral gap is larger than that of hyperbolic n-space? Even for surfaces (i.e n=2), many of these extremal problems are open. In this case, answers to these questions also provide insight into the shape of deformation spaces of hyperbolic surfaces. In these lectures, I will discuss some of these problems. I will talk about what is known about them and how random constructions of hyperbolic manifolds sometimes provide answers.
2020-08-24 / 10:30 ~ 11:30
학과 세미나/콜로퀴엄 - 콜로퀴엄: Arthur packets for certain cubic unipotent representations of G2 인쇄
by 장칭(KAIST)
Arthur packets are certain generalizations of L-packets. Arthur and several others constructed Arthur packets for classical groups. Following ideas of the work of Adams-Barbasch-Vogan on Archimedean groups, Cunningham et al. proposed a purely local way to construct Arthur packets for any algebraic reductive group over p-adic fields. In this talk, I will introduce Cunningham’s proposal using one example for the exceptional group G2. This is a joint work with Cunningham and Fiori.
2020-08-19 / 10:30 ~ 11:30
학과 세미나/콜로퀴엄 - 콜로퀴엄: Holomorphy of adjoint L-function of GL(3) 인쇄
by 장칭()
Riemann zeta functions and Dirichlet L-functions are first several examples of L-functions. Automorphic L-functions are vast generalizations of these L-functions. In this talk, I will give a quick survey of these L-functions and some related topics, including our recent work on holomorphy of adjoint L-function for GL(3) joint with Joseph Hundley.
2020-08-20 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - 대수기하학: Ulrich complexity for cubic fourfolds 인쇄
by ()
Ulrich complexity for a given projective variety X, originally introduced to measure the complexity of polynomials by Bläser-Eisenbud-Schreyer, is defined as the smallest possible rank for the Ulrich sheaves on X. The existence of an Ulrich sheaf on any hypersurface is well-known, however, Ulrich complexity is not very well understood even for cubic hypersurfaces. In this talk, I will review some recent studies on Ulrich complexity for small cubics, in particular, for smooth cubic fourfolds. This is a joint work in progress with D. Faenzi.
Events for the 취소된 행사 포함 모두인쇄
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