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Seminars and Colloquia

Algebra Seminar

Apr 6

01:20 pm

Exley Science Center Tower ESC 618

Cameron Hill, Wesleyan Somethoughts on probability measures as varieties. Abstract: There arespecial infinite structures (graphs and hyper-graphs) that reflect theasymptotic first-order properties of their finite induced substructures very,very accurately. Exactly what makes these infinite structures special can bedescribed model-theoretically in terms super-simplicity or in terms of higheramalgamation properties of the finite substructures. Using machinery fromfunctional analysis, I have proved that model-theoretic specialness yieldscertain nice probability measures with which you then perform your asymptoticanalyses. I dont fully understand what these measures are really like, and Iimagine that some algebraic geometry might provide a more concretetransformation from higher amalgamation properties to measures. I will describea possible set up for this.

Feb 16

01:20 pm

Exley Science Center Tower ESC 618

一道本不卡免费高清 Wai Kiu Chan, Wesleyan Warings problem for integral quadratic forms Abstract :For every positive integer n , let g ( n ) be the smallestinteger such that if an integral quadratic form in n variables can be written as a sum of squares of integral linear forms,then it can be written as a sum of g ( n ) squares of integral linear forms. Asa generalization of Lagranges Four-Square Theorem, Mordell (1930) showed that g (2) = 5 and later that year Ko (1930)showed that g ( n ) = n + 3 when n 5. More than sixty years later, M.-H. Kim and B.-K. Oh (1996) showed that g (6) = 10, and later (2005) they showedthat the growth of g ( n ) is at most an exponential of n . In this talk, I will discuss a recentimprovement of Kim and Oh's result showing that the growth of g ( n )is at most an exponential of $\sqrt{n}$. . This is a joint work with Constantin Beli, MariaIcaza, and Jingbo Liu.

Nov 3

01:20 pm

Exley Science Center Tower ESC 618

一道本不卡免费高清 Jonathan Huang, Wes A Macdonald formula for zeta functions ofvarieties over finite fields Abstract :We provide a formula for the generatingseries of the zeta function Z ( X , t )of symmetric powers Sym n X of varieties over finite fields. Thisrealizes Z ( X , t ) as an exponentiablemotivic measure whose associated Kapranov motivic zeta function takes values in W ( R )the big Witt ring of R = W ( ).We apply our formula to compute Z (Sym n X , t ) in a number ofexplicit cases. Moreover, we show that all -ringmotivic measures have zeta functions which are exponentiable. In this setting, theformula for Z ( X , t ) takes the form of aMacDonald formula for the zeta function.

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