Oscar Garcia-Prada, ICMAT, Madrid
‘'Involutions of Higgs bundle moduli spaces”
Asif Zaman, Department of Mathematics, University of Toronto
“Bounding the least prime in an arithmetic progression”
Mohammad Mahmoud, Pure Mathematics, University of Waterloo
"A Class of Structures without a Turing Ordinal"
We continue to show that the class Kw has no Turing Ordinal. We construct a set D which is not enumeration reducible to R_\A for any structure \A in Kw. This will imply directly that if the Turing ordinal exists then it must be strictly greater than 0. On the other hand Joe Miller showed that, for our class, if the Turing Ordinal exists it must be 0. Both statements tell us that the Turing Ordinal can't exist.
Ehsaan Hossain, Pure Mathematics, University of Waterloo
"The Invariant Basis Number Property"
Shuntaro Yamagishi, Pure Mathematics, University of Waterloo
"Some additive results in $\mathbb{F}_q[t]$"
We collected several results in $\mathbb{Z}$ of additive number theory and translated to results in $\mathbb{F}_q[t]$. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, diophantine approximation of polynomials over $\mathbb{Z}$ satisfying divisibility conditions, and the problem of Sidon regarding existence of certain thin sequences.
Chantal David, Concordia University
“Averages of Euler products and statistics of elliptic curves
Joint work with D. Koukoulopoulos and E. Smith.”
Raymond Cheng, Pure Mathematics, University of Waterloo
"Gutting Bundles on Tori"
Patrick Dornian, Combinatorics and Optimization, University of Waterloo
"Disproving the Hirsch Conjecture"
Richard Mack, Pure Mathematics, University of Waterloo
"Dual spaces and von Neumann Algebras"
A canonical construction in Linear Algebra is that of the dual space.
In this talk, we consider two questions:
When is a Banach space a dual space?
When is there only one possible predual?
Examples will be presented illustrating that these are not trivial questions, and a major theorem (Sakai's) will be presented giving a broad class of examples for the second question.
Stanley Burris, Pure Mathematics, University of Waterloo
"An Introduction to Boole's Algebra of Logic for Classes"
Boole's mysterious algebra of logic, based on the algebra of numbers and idempotent variables, has only been properly understood and justified in the last 40 years, more than a century after Boole published his most famous work, Laws of Thought. In this talk an elementary and natural development of Boole's system, from his partial algebra models up to his four main theorems, will be presented.