Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 3, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2014          October 2014          November 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6             1  2  3  4                      1
7  8  9 10 11 12 13    5  6  7  8  9 10 11    2  3  4  5  6  7  8
14 15 16 17 18 19 20   12 13 14 15 16 17 18    9 10 11 12 13 14 15
21 22 23 24 25 26 27   19 20 21 22 23 24 25   16 17 18 19 20 21 22
28 29 30               26 27 28 29 30 31      23 24 25 26 27 28 29
30


Friday, October 3, 2014

4:00 pm in 343 Altgeld Hall,Friday, October 3, 2014

#### Numerical computations and Galois groups in Schubert calculus

###### Abraham Martín del Campo   [email] (IST Austria)

Abstract: Schubert calculus is an important class of geometric problems involving linear spaces meeting other fixed but general linear spaces. Problems in Schubert calculus can be modeled by systems of polynomial equations. Thus, we can use numerical methods to find the solutions to these geometrical problems. We present a Macaulay2 implementation of numerical algorithms that solve Schubert problems. These algorithms are based on the geometric Pieri and Littlewood-Richardson homotopies. We use our implementation to study Galois groups of Schubert problems. This work is partially joint with Anton Leykin and Frank Sottile.

4:00 pm in 243 Altgeld Hall,Friday, October 3, 2014

#### A (not so witty) Introduction to Witt Rings.

###### Juan Villeta-Garcia (UIUC Math)

Abstract: Classically, work of Ernst Witt associates to a commutative ring $A$ a set of vectors together with a ring structure on them. This Witt" ring $W(A)$ encodes information about the original ring A, similar in spirit to the relationship between the $p$-adic integers and $\mathbb{Z}$. For example, work of Hesselholt and Madsen in the 90s found deep connections between the Topological Hochschild Homology (and consequently the algebraic K-Theory) of (certain) rings and their associated Witt rings. In this talk we will give a brief survey of the theory of Witt rings.