Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 2, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 2, 2017

11:00 am in 241 Altgeld Hall,Thursday, November 2, 2017

Even and Odd Minkowski Question Mark Functions

Chris Linden (UIUC Math)

Abstract: We introduce and discuss analogues of Minkowski's question mark function ?(x) related to continued fraction expansions with even or odd partial quotients. We prove that these functions are H\"older continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.

12:30 pm in 222 Loomis,Thursday, November 2, 2017

To Be Announced

Ronak Soni (TIFR, Mumbai)

2:00 pm in 241 Altgeld Hall,Thursday, November 2, 2017

RAMANUJAN’S LOST NOTEBOOK: HISTORY AND SURVEY

Bruce Berndt   [email] (UIUC)

Abstract: In the spring of 1976, while searching through papers of the late G. N. Watson at Trinity College, Cambridge, George Andrews found a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan, generally regarded as India’s greatest mathematician. In view of the fame of Ramanujan’s earlier notebooks, Andrews naturally called these papers Ramanujan’s “lost notebook.” This work, comprising about 650 results with no proofs, arises from the last year of Ramanujan’s life, and represents some of his deepest work. First, we provide a history of the lost notebook. Second, a general description of the contents of the lost notebook will be provided. Third, the remainder of the lecture will be devoted to a survey of some of the most interesting entries in the lost notebook. These include claims in q-series, theta functions, continued fractions, integrals, partitions, and other infinite series.

3:00 pm in 345 Altgeld Hall,Thursday, November 2, 2017

Integrability of generalized Toda lattice systems

Matej Penciak (Illinois)

Abstract: In this talk I will define a collection of integrable systems depending on a Lie algebra g called generalized Toda lattice systems. In the case when = sl_n, this system recovers the definition of the periodic Toda lattice. I will then describe Kostant's proof of the integrability of the generalized Toda lattice, working through the sl_n example along the way.

4:00 pm in 314 Altgeld Hall; followed by reception, 5-6 pm, 239 Altgeld Hall,Thursday, November 2, 2017

Four colors suffice

Robin J. Wilson (Open University and Gresham College)

Abstract: In this talk I present the history and solution of the four-color problem: Can every map be colored with just four colors so that neighboring countries are colored differently? The solution took 124 years to find, and used 1200 hours of computer time. But what did it involve, is it really a solution, and what role did the University of Illinois play in solving the problem? This illustrated lecture is open to anyone interested in this fascinating (and colorful) topic. $$ $$ Robin Wilson is an Emeritus Professor of Pure Mathematics at the Open University, Emeritus Professor of Geometry at Gresham College, London, and a former Fellow of Keble College, Oxford University. He is currently a Visiting Professor at the London School of Economics. A former President of the British Society for the History of Mathematics, he has written and edited about 40 books on the history of mathematics, including 'Lewis Carroll in Numberland', and also on graph theory, including 'Introduction to Graph Theory' and 'Four Colours Suffice'. Involved with the popularization and communication of mathematics and its history, he has been awarded the Mathematical Association of America’s Lester Ford award and Pólya prize for his ‘outstanding expository writing’.