Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 3, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2017          November 2017          December 2017
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  7             1  2  3  4                   1  2
8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
31


Friday, November 3, 2017

12:00 pm in 245 Altgeld Hall,Friday, November 3, 2017

#### To Be Announced

###### Kimberly Duran (UIUC)

3:00 pm in 341 Altgeld Hall,Friday, November 3, 2017

#### On the Gorensteinization of Schubert varieties via boundary divisors

###### Sergio Da Silva (Cornell University)

Abstract: A variety being Gorenstein can be a useful property to have when considering questions in birational geometry. Although Schubert varieties are Cohen-Macaulay, they are not Gorenstein in general. I will describe a convenient way to find a "Gorensteinization" for a Schubert variety by considering only one blow-up along its boundary divisor. We start by reducing to the local question, one involving Kazhdan-Lusztig varieties. These affine varieties can be degenerated to a toric variety defined using the Stanley-Reisner ideal of a subword complex. The blow-up of this variety along its boundary is now Gorenstein. Carefully choosing a degeneration of the blow-up allows us to extend this result to Schubert varieties.

4:00 pm in Knight Auditorium, Spurlock Museum; followed by reception, 5pm-7pm, Ballroom, Alice Campbell Alumni Center,Friday, November 3, 2017

#### Graph coloring and machine proofs in computer science, 1977-2017

###### Andrew W. Appel (Eugene Higgins Professor of Computer Science, Princeton University)

Abstract: The Four Color Theorem of Kenneth Appel and Wolfgang Haken (1976) was proved and checked with the assistance of computer programs, though much of the proof was written (and refereed) only by humans. Contemporaneously, Edinburgh LCF (Logic for Computable Functions) was developed by Robin Milner--a system for proofs written by humans (with computer assistance) but completely checked by computer; with particular application to proofs about computer programs. These two developments, and their convergence, have had significant impact on computer science, and my own research career: graph-coloring algorithms for register allocation in compilers, functional programming languages, fully machine-checked proofs of mathematical theorems, fully machine-checked proofs of software systems. One result at the intersection of all these is a machine-checked proof of correctness of a program that does register allocation by graph-coloring, using an algorithm related to one used in every four-color proof (and attempted proof) since 1879.