Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 23, 2014.

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events for the
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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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1  2  3  4  5  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
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Thursday, January 23, 2014

1:00 pm in Altgeld Hall 347,Thursday, January 23, 2014

#### Organizational meeting

2:00 pm in 140 Henry Administration Building,Thursday, January 23, 2014

#### Hecke polynomials and distinguishability of eigenforms of higher level

###### Alex Ghitza (University of Melbourne, Australia)

Abstract: A popular way of specifying a modular form is by giving its Fourier expansion. However, this is an infinite power series, so for practical purposes we are interested in questions such as: given two eigenforms, how many Fourier coefficients do we have to compare in order to distinguish the forms? I will describe some theoretical and computational results, and give a simple relation between this question and the properties of the Hecke polynomials of spaces of modular forms. Most of the work is joint with Sam Chow (Bristol) and James Withers (Boston University).

4:00 pm in 245 Altgeld Hall,Thursday, January 23, 2014

#### Free Resolutions and Symmetry

###### Steven V. Sam (University of California at Berkeley)

Abstract: This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.