Events

Brandon Doherty, Department of Pure Mathematics, University of Waterloo

"Goodstein sequences and the Hydra game"

Gödel's incompleteness theorem proves the existence of certain statements about the natural numbers that can be neither proven nor disproven using basic first-order arithmetic. The kinds of statements constructed in the standard proof of the incompleteness theorem, however, are extremely technical, and not very interesting in and of themselves. 

Adam Morgan, Department of Applied Mathematics, University of Waterloo

"Finite Element Exterior Calculus, Part 3"

We will finish covering the concepts intended for the previous week's lecture, introducing discretizations of de Rham complexes and some rudimentary definitions in finite element analysis.

MC 5417

David Urbanik, University of Waterloo

"What is a reciprocity law?"

There are numerous theorems in algebraic number theory which are "reciprocity laws". The simplest of these is quadratic reciprocity, for which there are many elementary proofs. For higher powers, there are many similar-looking statements, but whose proofs become progressively harder. We survey a number of reciprocity laws, give proofs of some simple ones, and try to show that they are all related.

MC 5403

Leanne Stuive,  Department of Combinatorics & Optimization, University of Waterloo

"Approximating Convex Bodies by Polytopes"

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"The Homological Algebra of PDEs"

Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo

"More about morphisms of schemes"

We will continue with the discussion about morphisms of schemes. We  
will see an explicit example of constructing morphisms of schemes by  
cutting up into affine open sets and then gluing them together. Then, we  
will define $Z$-valued points, where $Z$ is a given scheme. This  
notion will lead us to determine a morphism not by its values at points  
but rather by its induced map of $Z$-valued points.

Tristan Freiberg, Pure Mathematics, University of Waterloo

"Distribution of primes in intervals"

Akshaa Vatwani, Department of Pure Mathematics, University of Waterloo

"Variants of equidistribution in arithmetic progressions"

It is well known that the prime numbers are equidistributed in arithmetic progressions. Such a phenomenon is also observed more generally for a class of multiplicative functions. We derive some variants of such results and give a few applications. We also discuss an interesting application that relates to the Chowla conjecture on correlations of the Mobius function, and show its relevance to the twin prime conjecture.

Rick Kun-Hung Hsueh, Department of Pure Mathematics, University of Waterloo

"An analogy between classical and free Brownian motion: A combinatorial approach"

The first part of the talk deals with how plane integer lattice paths can be exploited to calculate moments of random variables of the form A + B, where A, B are linear operators defined on the the full Fock space. In particular, this covers the cases for Gaussian and Wigner semicircle laws which are indispensable parts for classical and free Brownian motion.

All talks will take place in MC 5403.

13:00-14:00

Spectral flow and the Riesz stability of the Atiyah-Singer Dirac operator under bounded perturbations of local boundary conditions.

Lashi Bandara, Universität Potsdam