Infosheet (February 7th, 2017) 
Queen's University  Department of Mathematics and Statistics 
Tuesday, February 7 
Grad Seminar Time: 12:30 p.m. Place: Jeffery 115 
Speaker: Siddhi Pathak Title: A historical introduction to special values of Lfunctions Abstract Attached 
Tuesday, February 7 
Seminar in Free Probability and Random Matrices Time: 2:30 p.m. Place: Jeffery 222 
Speaker: Josué Daniel Vázquez Becerra, Queen’s University Title: The effect of asymptotic liberation on the covariance of traces of random matrices, II Abstract Attached 
Tuesday, February 7 
Dynamics Seminar Time: 3:30 p.m. Place: Jeffery 422 
Speaker: Francesco Cellarosi, Queen’s University Title: Furstenberg’s proof of Szemeredi’s theorem (Part 2) Abstract Attached 
Thursday, February 9 
Math Club Time: 5:30 p.m. Place: Jeffery 118 
Speaker: M. Ram Murty Title: When does a prime divide a binomial coefficient? Abstract Attached 
Friday, February 10 
Number Theory Seminar Time: 10:30 a.m. Place: Jeffery 422 
Speaker: Akshaa Vatwani, University of Waterloo Title: TBA

Friday, February 10 
Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 
Speaker: Vaidehee Thatte, Queen’s University Title: Ramification theory for arbitrary valuation rings in positive characteristic Abstract Attached 
Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.
Tuesday, February 7, 12:30 p.m. Jeffery 115  Grad Seminar
Speaker: Siddhi Pathak
Title: A historical introduction to special values of Lfunctions
Abstract: We will describe the historical development of the theory, focusing on work before the twentieth century.
Tuesday, February 7, 2:30 p.m. Jeffery 222
Seminar in Free Probability and Random Matrices
Speaker: Josué Daniel Vázquez Becerra
Title: The effect of asymptotic liberation on the covariance of traces of random matrices, II
Abstract: In this talk, we present some estimations for the asymptotic behaviour of the covariance of (unnormalized) traces of random matrices, when conjugated by asymptotically liberating random unitary matrices.
Seminar website: http://www.mast.queensu.ca/~mingo/seminar/
Tuesday, February 7, 3:30 p.m. Jeffery 422  Dynamics Seminar
Speaker: Francesco Cellarosi
Title: Furstenberg’s proof of Szemeredi’s theorem (Part 2)
Abstract: In this expository talk, I will present the ergodictheoretic proof of a famous theorem of E. Szemerédi. The theorem (proved in 1975, and previously known as a conjecture of P. Erdős and P. Turán) states that every set of integers with positive upper density contains arbitrary long arithmetic progressions. After the original combinatorial proof, H. Furstenberg found a different proof in 1977, using ergodic theory. He noticed that Szemerédi's theorem is equivalent to a statement about multiple recurrence of measure preserving transformations. I will explain the main ideas in the proof, and in particular why multiple recurrence occurs for special classes of examples: Bernoulli systems, and weakly mixing systems. The talk is based on a 1982 paper by H. Furstenberg, Y, Katznelson and D. Ornstein.
Thursday, February 9, 5:30 p.m. Jeffery 118  Math Club
Speaker: M. Ram Murty
Title: When does a prime divide a binomial coefficient?
Abstract:
We will use elementary number theory to answer the question in the title
and also relate
the question to padic numbers.
Friday, February 10, 2:30 p.m. Jeffery 234  Department Colloquium
Speaker: Vaidehee Thatte
Title: Ramification theory for arbitrary valuation rings in positive characteristic
Abstract: Our goal is to develop ramification theory for arbitrary valuation fields, that is compatible with the classical theory of complete discrete valuation fields with perfect residue fields. We consider fields with more general (possibly nondiscrete) valuations and arbitrary (possibly imperfect) residue fields. The defect case, i.e., the case where there is no extension of either the residue field or the value group, gives rise to many interesting complications.We present some new results for ArtinSchreier extensions of valuation fields in positive characteristic. These results relate the "higher ramification ideal" of the extension with the ideal generated by the inverses of ArtinSchreier generators via the norm map. We also introduce a generalization and further refinement of Kato's refined Swan conductor in this case. Similar results are true in the mixed characteristic case.