Thursday, November 4, 2021

2021-11-11 / 17:00 ~ 18:00

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Let  C⊂P^r be a nondegenerate projective integral curve of degree d and arithmetic genus g. A celebrated theorem of Castelnuovo gives an explicit upper bound pi_0(d,r) on g in terms of d and n. Moreover, if d ≥ 2r+1 then g=pi_0 (d,r) if and only if C is ACM and it lies on a surface of minimal degree. In 1980, Joe Harris and David Eisenbud proved that (i) C lies on a surface of minimal degree if g> pi_1 (d,r), and (ii) if g=pi_1(d,r) and C does not lie on a surface of minimal degree, then there exists a del Pezzo surface which contains C. Along this line, we will show that there exists an integer pi_1(d,r)^' < pi_1(d,r) such that  C lies on a del Pezzo surface if g> pi_1(d,r)^' This is a joint work with Wanseok Lee

2021-11-11 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

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In this talk we consider the Waring rank of monomials over the rational numbers. We give a new upper bound for it by establishing a way in which one can take a structured apolar set for any given monomial. This bound coincides with all the known cases for the real rank of monomials, and is sharper than any other known bounds for the real Waring rank. Since all of the constructions are still valid over the rational numbers, this provides a new result for the rational Waring rank of any monomial as well. We also apply the methods developed in the paper to the problem of finding an explicit rational Waring decomposition of any homogeneous polynomial over rational numbers, which is important in many applications, especially to the integration of a polynomial over a simplex. We will present examples and computational implementation for potential use.

2021-11-10 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - PDE 세미나:

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This series of lectures will focus on recent developments of the so-called a-contraction theory and its application to the study of discontinuous flow at high Reynolds numbers. We will first introduce the classical framework to study the stability of 1D shocks for compressible flows. Recent multi-D applications will be presented next, both in the context of compressible and incompressible flows.

2021-11-09 / 09:30 ~ 12:00

학과 세미나/콜로퀴엄 - 정수론:

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KAIX Distinguished lectures in Mathematics Speaker : Wen-Ching Winnie Li (Distinguished Professor of Mathematics, Penn. State Univ.) 2021.11.09 (Tue) - Korean time 09:30-10:30 Colloquium talk Primes in Number Theory and Combinatorics 10:30-10:50 Q&A 11:00-12:00(noon) Seminar Talk Pair arithmetical equivalence for quadratic fields ZOOM ID : 518 127 6292 (No password required) Abstract: 1. colloquium talk Title: Primes in number theory and combinatorics Abstract: Prime numbers are a central topic in number theory. They have inspired the study of many subjects in mathematics. Regarding prime numbers as the building blocks of the multiplicative structure of positive integers, in this survey talk we shall interpret "primes" as the basic elements in a structure of interest arising from combinatorics and number theory, and explore their distributions of various kinds. More precisely, we shall examine primes in compact Riemann surfaces, graphs, and 2-dimensional simplicial complexes, respectively. These results are products of rich interplay between number theory and combinatorics. 2. number theory seminar talk Title: Pair arithmetical equivalence for quadratic fields Abstract: Given two nonisomorphic number fields K and M, and two finite order Hecke characters $\chi$ of K and $\eta$ of M respectively, we say that the pairs $(\chi, K)$ and $(\eta, M)$ are arithmetically equivalent if the associated L-functions coincide: $L(s, \chi, K) = L(s, \eta, M)$. When the characters are trivial, this reduces to the question of fields with the same Dedekind zeta function, investigated by Gassmann in 1926, who found such fields of degree 180, and by Perlis in 1977 and others, who showed that there are no arithmetically equivalent fields of degree less than 7. In this talk we discuss arithmetically equivalent pairs where the fields are quadratic. They give rise to dihedral automorphic forms induced from characters of different quadratic fields. We characterize when a given pair is arithmetically equivalent to another pair, explicitly construct such pairs for infinitely many quadratic extensions with odd class number, and classify such characters of order 2. This is a joint work with Zeev Rudnick.

2021-11-08 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

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In my next talk, I will define canonical dimension of varieties (which, roughly speaking, measures how hard it is to get a rational point in a given variety) and canonical dimension of algebraic groups (which, roughly speaking, measures how complicated the torrsors of an algebraic group can be). Then I will state several previously known facts from intersection theory and from theory of canonical dimension, and I will prove that if we know that a certain product of Schubert divisors is mutiplicity-free (which was defined in my first talk), then this fact implies an upper estimate on the canonical dimension of the group and its torsors. As a result, we will get some explicit numerical estimates on canonical dimension of simply connected simple split algebraic groups groups with simply-laced Dynkin diagrams.

2021-11-05 / 09:30 ~ 16:20

SAARC 세미나 - SAARC 세미나:

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2021-11-04 / 09:30 ~ 16:20

SAARC 세미나 - SAARC 세미나:

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2021-11-04 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 박기호(고등과학원)

We will survey recent development in subadditive thermodynamic formalism for matrix cocycles. In particular, in the setting of locally constant cocycles as well as fiber-bunched cocycles, we will discuss sufficient conditions for the norm potentials of such cocycles to have unique equilibrium states. If time permitting, we will also discuss ergodic properties of such equilibrium states as well as some applications.

2021-11-05 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 대수기하학: Twisted equivalences in spectral algebraic geometry I

by 조창연(서울대학교 QSMS)

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 talk 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; in particular, some familiarity with ordinary algebraic geometry will be enough for the talk.

2021-11-11 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

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Abstract: From fertilization to birth, successful mammalian reproduction relies on interactions of elastic structures with a fluid environment. Sperm flagella must move through cervical mucus to the uterus and into the oviduct, where fertilization occurs. In fact, some sperm may adhere to oviductal epithelia, and must change their pattern of oscillation to escape. In addition, coordinated beating of oviductal cilia also drive the flow. Sperm-egg penetration, transport of the fertilized ovum from the oviduct to its implantation in the uterus and, indeed, birth itself are rich examples of elasto-hydrodynamic coupling. We will discuss successes and challenges in the mathematical and computational modeling of the biofluids of reproduction.

2021-11-11 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론: On Euler systems for the multiplicative group over general number fields

by Prof. Soogil Seo(Yonsei University)

We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning higher rank Euler systems for the multiplicative group over arbitrary number fields. This is a joint work with Burns, Daoud, and Sano.

2021-11-09 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: 2-complexes with unique embeddings in 3-space

by 김재훈(KAIST)

A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem. This is joint work with Agelos Georgakopoulos.

2021-11-04 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: On a conjecture of Coleman concerning Euler systems

by 서수길(연세대학교)

We introduce a distribution-theoretic conjecture of Roert Coleman of the 1980's and prove the conjecture in a recent joint work with Burns and Daoud. This accordingly gives an explicit description of the complete set of Euler systems for the multiplicative group over Q together with a connection to other conjectures in number theory.

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