Thursday, August 13, 2020

2020-08-19 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 위상수학 세미나: Extremal problems and probabilistic methods in hyperbolic geometry

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.

2020-08-19 / 10:30 ~ 11:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Holomorphy of adjoint L-function of GL(3)

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.

2020-08-13 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 학부생 콜로퀴엄:

by ()

In this talk, I will show that secant varieties of a smooth projective curve embedded by a sufficiently large degree has normal Cohen-Macaulay Du Bois singularities. I will also prove that the curve is rational if and only if any secant variety has log terminal singularities, and the curve is elliptic if and only if any secant variety has log canonical singularities that are not log terminal (not even rational). This talk is based on joint work with Lawrence Ein and Wenbo Niu.

2020-08-20 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Ulrich complexity for cubic fourfolds

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.

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