Events

Wentang Kuo, Department of Pure Mathematics, University of Waterloo

"On Erd}os-Pomerance conjecture"

Let k be a global function eld whose eld of constants is the nite eld Fq. Let 1 be a xed place of degree one, and A is the ring of elements of k which have only 1 as a pole. Let be a sgn-normalized rank one Drinfeld A-module dened over O, the integral closure of A in the Hilbert class eld of A. We prove an analogue of a conjecture of Erd}os and Pomerance for '.

Robert Garbary, Department of Pure Mathematics, University of Waterloo

"Parametrizing Points on Algebraic Curves"

Algebraic Geometry is the study of subsets of kn (here, k is a field) defined by the vanishing of polynomial equations - these objects are called algebraic varieties. For example, the circle S1 R2 is an algebraic variety (over R) since it is precisely the zero locus of the polynomial x2+y2 1 2 R[x; y]. The circle is an example of a plane curve - the vanishing of a single polynomial inside the plane k2. These objects get complicated very quickly.

Elcim Elgun, Department of Pure Mathematics, University of Waterloo

"The Eberlein Compactication of the Heisenberg Type Group Z T T"

Given a locally compact group G, the Eberlein compactication Ge is the spectrum of the uniform closure of the Fourier-Stieltjes algebra B(G). It is a semitopological semigroup compactication and thus a quotient of the weakly almost periodic compactication of G.

Harm Derksen, University of Michigan

“Tensor Rank”

The notion of the rank of a matrix can be generalized to the rank of higher order tensors. This notion has many theoretical and practical applications. For example, the complexity of multiplying matrices is closely related to the rank of certain tensors. In signal processing, one would like to approximate tensors with tensors of low rank.

Eva Leenknegt, Purdue University

“Properties of functions in P-minimal structures”

The concept of P-minimality was developed by Haskell and MacPherson as a version of o-minimality for the p-adics. This should be thought of as a ’tame’ context, where one may hope that definable functions will have better properties than general p-adic functions.

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s Theorem: Part II”

We'll continue our look at Gromov's theorem and consider the case of solvable groups. In particular, we will begin the proof that a finitely generated solvable group of polynomially bounded growth is nilpotent-by-finite. It is again my hope that the lecture will be accessible to a general audience.

John Loftin, Rutgers University Newark

“Minimal Lagrangian Surfaces in CH2”

An immersed minimal Lagrangian surface in the complex hyperbolic plane CH2 inherits a conformal structure from the induced metric. Moreover, the components of the second fundamental form can be written in terms of a cubic differential U which is holomorphic with respect to the conformal structure.

Robert Garbary, Department of Pure Mathematics, University of Waterloo

“Linearizing a smooth map”

I’m going to continue talking about the tangent spaces of a manifold. Given a smooth map f :M →N andapointp∈M,we’regoingtoconstructalinearmapfp :TpM →Tf(p)N -it’s this crazy thing you may have heard about before called the ’chain rule’. I will go through an explicit example or two in painstaking detail, and talk about why we care about points where this map has rank 0.

Ian Payne, Department of Pure Mathematics, University of Waterloo

“Necessary Conditions for Graphs with Taylor Polymorphisms”

Even cycles with constants of length at least 6 are a class of graphs having no Taylor polymorphism. In trying to generalize this, I managed to show that the same holds for any bipartite graph of even girth (at least 8) with one additional magic property.

Mahmood Alaghmandan, University of Saskatchewan

“Hypergroups and some questions in abstract harmonic analysis”

Hypergroups as a generalized version of locally compact groups have similarities with topological groups. Emphasizing some of these similarities, we define and study Følner type conditions for hypergroups. We also observe some results obtained from Leptin condition for Banach algebras defined on hypergroups, namely hypergroup algebras and Fourier algebras.

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Number Theory seminar

Wentang Kuo, Department of Pure Mathematics, University of Waterloo

"On Erd}os-Pomerance conjecture"

Student colloquium

Robert Garbary, Department of Pure Mathematics, University of Waterloo

"Parametrizing Points on Algebraic Curves"

Analysis seminar

Elcim Elgun, Department of Pure Mathematics, University of Waterloo

"The Eberlein Compactication of the Heisenberg Type Group Z T T"

Pure Math colloquium

Harm Derksen, University of Michigan

“Tensor Rank”

Logic seminar

Eva Leenknegt, Purdue University

“Properties of functions in P-minimal structures”

Algebra seminar

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s Theorem: Part II”

Geometry & Topology seminar

John Loftin, Rutgers University Newark

“Minimal Lagrangian Surfaces in CH2”

Grad student Geometry and Topology learning seminar

Robert Garbary, Department of Pure Mathematics, University of Waterloo

“Linearizing a smooth map”

Universal Algebra seminar

Ian Payne, Department of Pure Mathematics, University of Waterloo

“Necessary Conditions for Graphs with Taylor Polymorphisms”

Analysis seminar

Mahmood Alaghmandan, University of Saskatchewan

“Hypergroups and some questions in abstract harmonic analysis”

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