세미나 및 콜로퀴엄

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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

Among the most well-known examples of L-functions are the Riemann zeta
function and the L-functions associated to classical modular forms.
Less well known, but equally important, are the L-functions associated
to Maass forms, which are eigenfunctions of the Laplace-Beltrami
operator on a hyperbolic surface. Named after H. Maass, who discovered
some examples in the 1940s, Maass forms remain largely mysterious.

Fortunately, there are concrete tools to study Maass forms: trace
formulas, which relate the spectrum of the Laplace operator on a
hyperbolic surface to its geometry. After Selberg introduced his
famous trace formula in 1956, his ideas were generalised, and various
trace formulas have been constructed and studied. However, there are
few numerical results from trace formulas, the main obstacle being
their complexity. Various types of trace formulas are investigated,
constructed and used to understand automorphic representations and
their L-functions from a theoretical point of view, but most are not
explicit enough to implement in computer code.

Having explicit computations of trace formulas makes many potential
applications accessible. In this talk, I will explain the
computational aspects of the Selberg trace formula for GL(2) for
general levels and applications towards the Selberg eigenvalue
conjecture and classification of 2-dimensional Artin representations
of small conductor.
This is a joint work with Andrew Booker and Andreas Strömbergsson.

Host: 임보해     영어     2017-03-02 11:08:35

In this talk, we summarize results concerning anomalous behaviour of random walks and diffusions in disordered media. Examples of disordered media include fractals and various models of random graphs, such as percolation clusters, random conductance models, ErdH{o}s-R'enyi random graphs and uniform spanning trees.

Geometric properties of such disordered media have been studied extensively and their scaling limits have been obtained. Our focus here is to analyze properties of dynamics in such media. Due to the inhomogeneity of the underlying spaces, we observe anomalous behaviour of the heat kernels and obtain anomalous diffusions as scaling limits of the random walks. We will give a chronological overview of the related research, and describe how the techniques have developed from those introduced for exactly self-similar fractals to the more robust arguments required for random graphs.

 

 

Host: 폴정     영어     2017-02-21 12:35:16

2017 제2회 정오의 수학산책

 

 

 

강연자: 이윤원 (인하대)

일시: 2017년 4월 28일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

 

제목: Atiyah-Singer index theorem

내용: TBA

 

등록: 2017년 4월 26일(수) 오후 3시까지

        https://goo.gl/forms/0lqSboiW5A9vv9rd2

 

문의: hskim@kias.re.kr / 내선:8545

 

 

Host: 이지운     한국어     2017-02-28 16:12:46

This talk will review previous work on quadrupedal gaits and recent work on a generalized model for binocular rivalry proposed by Hugh Wilson. Both applications show how rigid phase-shift synchrony in periodic solutions of coupled systems of differential equations can help understand high level collective behavior in the nervous system.

 

 

Host: 김재경     영어     2017-02-21 12:38:07

2017 제3회 정오의 수학산책

 

 

 

강연자: 이수준(경희대)

일시: 2017년 5월 12일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

 

제목: 양자정보이론 소개 : 디지털정보 vs 양자정보

내용: TBA

 

등록: 2017년 5월 10일(수) 오후 3시까지

          https://goo.gl/forms/TnDIENKzVJAnxy9v2

 

문의: hskim@kias.re.kr / 내선:8545

 

Host: 이지운     한국어     2017-02-28 16:16:01

   In the talk, I discuss previous works on the arithmetic of various twisted special $L$-values and dynamical phenomena behind them. Main emphasis will be put on the problem of estimating several exponential sums such as Kloosterman sums and its relation to the problem of non-vanishing of special $L$-values with cyclotomic twists. A distribution of homological cycles on the modular curves will also be discussed and as a consequence, some results on a conjecture of Mazur-Rubin-Stein about the distribution of period integrals of elliptic modular forms will be presented.  

 
미정     2017-01-16 13:37:22