Department of

Mathematics


Seminar Calendar
for Illinois Geometry Lab events the year of Tuesday, March 13, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 23, 2018

5:00 pm in 314 Altgeld Hall,Tuesday, January 23, 2018

IGL Kickoff Meeting

Abstract: Spring 2018 organizational meeting for the Illinois Geometry Lab.

Thursday, March 15, 2018

5:00 pm in 314 Altgeld Hall,Thursday, March 15, 2018

IGL Mid-semester meeting

Abstract: Come see what the IGL research groups have been working on this semester! 5:00-6:30 followed by pizza.

Thursday, April 26, 2018

11:00 am in 241 Altgeld Hall,Thursday, April 26, 2018

The Unreasonable Effectiveness of Benford's Law in Mathematics

A J Hildebrand and Junxian Li (Illinois Math)

Abstract: We describe work with Zhaodong Cai, Matthew Faust, and Yuan Zhang that originated with some unexpected experimental discoveries made in an Illinois Geometry Lab undergraduate research project back in Fall 2015. Data compiled for this project suggested that Benford's Law (an empirical "law" that predicts the frequencies of leading digits in a numerical data set) is uncannily accurate when applied to many familiar mathematical sequences. For example, among the first billion Fibonacci numbers exactly 301029995 begin with digit 1, while the Benford prediction for this count is 301029995.66. The same holds for the first billion powers of 2, the first billion powers of 3, and the first billion powers of 5. Are these observations mere coincidences or part of some deeper phenomenon? In this talk, which is aimed at a broad audience, we describe our attempts at unraveling this mystery, a multi-year research adventure that turned out to be full of surprises, unexpected twists, and 180 degree turns, and that required unearthing nearly forgotten classical results as well as drawing on some of the deepest recent work in the area.

Thursday, May 3, 2018

1:00 pm in Illini Union Room A ,Thursday, May 3, 2018

Spring 2018 Open House

Abstract: The IGL end-of-semester Open House will take place from 1:00 pm to 4:00 pm in Room A at the Illini Union. Come see what the IGL teams have produced this semester!

Friday, September 21, 2018

4:00 pm in 245 Altgeld Hall,Friday, September 21, 2018

Computer Driven Questions and Theorems in Geometry

Moira Chas (Stony Brook)

Abstract: Three numbers can be associated to a deformation class of closed curves on a surface S:

- the self-intersection number (this is the smallest number of times a representative of the curve crosses itself),
- the word length (that is the smallest number of letters, in a certain alphabet chosen apriori, one needs to describe the class ) and
- the length of the geodesic in the class (this is the length of the shortest representative of the class, where the way of computing length is chosen beforhand).

The interrelations of these three numbers exhibit many patterns when explicitly determined or approximated using algorithms and a computer. We will discuss how these computations can lead to counterexamples of existing conjectures, to the discovery of new conjectures and to subsequent theorems in some cases.