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Events happening on October 13, 2015

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Oct. 13, 2015 5pm
Oct. 13, 2015 10am (Math350)	Fred Goodman (Iowa) X TBD Introduction to Cellular Algebras
Oct. 13, 2015 11am (MATH 350)	Number Theory Lillian Pierce (Duke University) X Fifty years ago Birch proved a landmark result on how many variables are required by the circle method in order to produce an asymptotic for the number of (simultaneous) representations of a fixed tuple of integers by a fixed system of forms of the same degree. While this result has not budged much since, some progress can be made in lowering the number of variables in certain cases. This talk will introduce new work for systems of 2 quadratic forms, joint with Roger Heath-Brown, and for systems of 3 quadratic forms, joint with Damaris Schindler and Melanie Wood, that brings the number of variables down if we relax our requirement to representing “almost every” tuple of integers. The key innovation is a multi-dimensional version of Kloosterman’s circle method, which allows us to harvest more cancellation from exponential sums on the minor arcs. This talk will discuss the advantages and difficulties of obtaining cancellation in oscillatory integrals and exponential sums, and will not assume extensive prior knowledge of the circle method. Integers represented by systems of quadratic forms
Oct. 13, 2015 12:10pm (MATH …	Kempner Lillian Pierce (Duke University) X Each number field (finite extension of the rationals) has an integer associated to it called the class number (the cardinality of the class group of the field). Class numbers are important objects that naturally occur in number theory, but many open questions remain about the growth and divisibility properties of class numbers of fields varying over an appropriate infinite family. We will survey some key conjectures and results since the pioneering work of Gauss, and then turn to new work on averages and moments for p-torsion in class groups of fields of degree 2, 3, 4 and 5. This includes joint work with Ellenberg, Heath-Brown, Thorne, and Wood. This talk will be accessible to a general math audience. Averages and moments associated to class numbers
Oct. 13, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The simplest polynomial time algorithm for CSPs: checking local consistency, Part 2
Oct. 13, 2015 1pm (Math350)	Sebastian Casalaina-Martin Complex geometry overview, part 3 of 3
Oct. 13, 2015 2pm (MATH 350)	Lie Theory Fred Goodman (Iowa) X I will discuss the construction of cellular bases for the Brauer algebras, BMW algebras, etc. which share many properties of the Murphy bases of the Hecke algebras of the symmetric groups. Murphy bases for algebras with a Jones basic construction
Oct. 13, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Oct. 13, 2015 3pm (Math 350)	Jonathan Wise (CU Boulder) X We'll revisit the idea of linear approximation in a way that allows us to talk about first-order approximations of quite general mathematical objects. We'll see in a few examples how first-order deformations can be classified using cohomology. Differentiation and linear approximation

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