Seminars in March 2013

• Mitsugu Hirasaka, Zeta functions of adjacecny algebras

  Zeta functions of adjacecny algebras

  Mitsugu Hirasaka
  Department of Mathematics,Pusan National University

  2013/03/29 Fri 4PM-5PM

  For a module L the formal Dirichlet series $\zeta$_L(s) = ∑_{n ≥ 1</i>}a_nn^-s is defined whenever the number a_n of submodules of L with index n is finite for each positive integer n. For a ring R and a finite association scheme (X,S) we denote the adjacency algebra of (X,S) over R by RS. In this talk we aim to compute $\zeta$_ZS(s) where $$ZS is regarded as a $$ZS-module under the assumption that $|X|$ is prime or $|S|=2$.</p>

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  • MitsuguHirasaka

• (ASARC seminar) Sang June Lee, Extremal results on combinatorial number theory

  FYI (ASARC seminar)

  Extremal results on combinatorial number theory

  Sang June Lee
  ASARC, KAIST

  2013/03/15 Thu 5PM-6PM

  In this talk we deal with extremal results on combinatorial number theory. A typical problem is as follows. We fix a family of linear equations (for example, a+b=2c or a+b=c+d). Then we want to estimate the maximum size of subsets with no solution of the given equations in {1,2,…,n} or a random subset of {1,2,…,n} of size m < n. We consider two important examples:</p>

  (1) Sets which contain no arithmetic progression of a fixed size

  (2) Sidon sets (without solutions of a+b=c+d)

  The first example is about the results of Roth in 1953 and Szemeredi in 1975, and the recent results by Schacht in 2009+, and Conlon-Gowers in 2010+.

  Next, the second example is about the results by Erdős, Turán, Chowla, Singer in 1940s and the results by Kohayakawa, Lee, Rödl, and Samotij in 2012+.

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