Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 17, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2014           September 2014          October 2014
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1  2       1  2  3  4  5  6             1  2  3  4
3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
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Wednesday, September 17, 2014

2:00 pm in 441 Altgeld Hall,Wednesday, September 17, 2014

#### Hilbert's Sixteenth Problem, Discriminants, and maybe Toric Varieties

###### Michael DiPasquale   [email] (UIUC Math)

Abstract: In the first part of his sixteenth problem, Hilbert asks for an investigation of the ways in which the components of a real plane algebraic curve of degree d can be arranged. This problem was part of the impetus for the development of what is now known as real algebraic geometry. In this talk we will highlight a few of the differences between real and complex algebraic geometry (sticking to the context of curves). We will discuss the solution to Hilbert's question in degree 6, which was finished in 1969. Furthermore, we will indicate how isotopy classes can be studied via discriminants. Time permitting, we will try to give an idea of how toric geometry can be used to classify certain isotopy classes.

3:00 pm in 347 Altgeld Hall,Wednesday, September 17, 2014

#### Vertex Algebras and Symmetric Functions

###### Maarten Bergvelt (UIUC)

Abstract: Vertex algebras are “singular commutative rings with translation symmetry”. I’ll give a hopefully gentle introduction. Then we turn to the ring Sym of symmetric functions. This ring carries many amazing and beautiful structures, among which is an action of the Lie algebra sl_2. Using this we find explicit formulas for the vertex algebra structure of Sym.

4:00 pm in 245 Altgeld Hall,Wednesday, September 17, 2014

#### What is Number Theory

###### Bruce Berndt (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: I will begin on a personal note and indicate how I became a number theorist. Second, the various kinds or branches of number theory will be briefly described. We next concentrate principally on analytic number theory. Most problems in the subject can be classified as either additive or multiplicative, and we briefly describe how different approaches are used. Lastly, some of the main areas in analytic number theory, along with some of the outstanding open problems, are described. In particular, we discuss partitions, sums of powers, and the divisor function.