Jonathan Herman, Department of Pure Mathematics, University of Waterloo
“Symplectic Reduction”
Jimmy He, Department of Pure Mathematics, University of Waterloo
“An Introduction to Equivariant Cohomology”
This talk will introduce equivariant cohomology with discussion of the Borel, Weil and Cartan constructions.
MC 5403
Satish Pandey, Department of Pure Mathematics, University of Waterloo
“Positive maps”
Ted Eaton, Combinatorics & Optimization, University of Waterloo
"The quantum random oracle model"
In cryptography, a common task is to reduce the problem of breaking an encryption or digital signature scheme to some underlying hard computational problem. This is similar to how complexity theorists reduce problems to one another to show that they are in the same complexity class.
These reductions can often be established more easily by considering different security models. A common model to employ is called the random oracle model.
Satish Pandey, Department of Pure Mathematics, University of Waterloo
“Positive maps continued”
Jonathan Herman, Department of Pure Mathematics, University of Waterloo
“The Marsden-Weinstein Theorem and Some Corollaries”
We will clean up the proof given last talk of the Marsden-Weinstein theorem. We will then prove both the Jacobi-Liouville theorem and the Krillov-Kostant-Souriau theorem as corollaries. Time permitting, we will introduce multi-momentum maps and their existence/uniqueness.
MC 5403
Arthur Mehta, Department of Pure Mathematics, University of Waterloo
"Positivstellensatz and semi-pre-C*-algebras"
A positivstellensatz can loosely be described as a characterisation of elements a in an algebra A that are positive under a certain class of representations. In this talk we review some classical results regarding positive polynomials and then look at a series of Positivstellensatz that can be obtained by using the framework of semi-pre-C*-algebras.
MC 5501
Per Salberger, Chalmers University of Technology
"Counting rational points on cubic curves"
We present a new uniform bound for the number of rational points of height at most B on non-singular cubic curves, which improves upon previous bounds of Ellenberg/Venkatesh and Heath-Brown/Testa.
M3 3103
Stanley Yao Xiao, Pure Mathematics, University of Waterloo
"Some results on binary forms and counting rational points on algebraic varieties"
Russell Miller, Queens College - City University of New York
"Hilbert's Tenth Problem for Subrings of the Rationals"