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Mathematics & Statistics

# Colloquia — Fall 2018

## Friday, November 16, 2018

Title
Speaker

Time
Place

Quasisymmetric Geometry of Fractal Spaces
Hrant Hakobyan
Kansas State University
3:00pm-4:00pm
CMC 130
Arthur Danielyan

Abstract

Koebe's mapping theorem states that every finitely connected domain in the plain can be mapped to a circle domain, i.e. a domain bounded by circles and points. Koebe's conjecture asks if it is true that in fact, every planar domain is conformal to a circle domain. Quasiconformal (QC) and Quasisymmetric (QS) mappings generalize conformal mappings to higher dimensions and thus one may wonder if the QC or QS versions of Koebe's conjecture are true. In this talk we will discuss when a topologically planar metric space (e.g., a domain or a Sierpinski carpet) is quasisymmetric to a planar set that is bounded by circles. In particular, we will describe several classes of metric spaces where a complete characterization is possible.

## Friday, November 2, 2018

Title
Speaker

Time
Place

Practical limitations of quantum algorithms for integer factorization
John Schanck
Institute for Quantum Computing
University of Waterloo
3:00pm-4:00pm
CMC 130
Jean-François Biasse

Abstract

Few of the submissions to NIST's post-quantum cryptography standardization effort are susceptible to known polynomial-time attacks. A notable exception is “Post-Quantum RSA”, which makes a security claim based on the difficulty of factoring (enormous) integers. While much of the motivation for post-quantum cryptography comes from Shor's quantum algorithm for integer factorization, there are still limits to the size of numbers that might be ever be factored — even under hugely optimistic assumptions about future technology. Post-Quantum RSA is unlikely to win NIST's approval, but a close analysis of the cost of factoring can tell us a lot about the cost of quantum computation in general. I'll discuss cost models for quantum computation and apply these models to Shor's algorithm. I'll then show how you can get a one million percent speedup in the prime generation step of terabyte-RSA key generation, with only a small decrease in security. I will not assume a background in quantum computing.

## Friday, October 19, 2018

Title
Speaker

Time
Place

Almost axisymmetric flows
Marc Sedjro
African Institute for Mathematical Sciences (AIMS)
Tanzania, Africa
3:00pm-4:00pm
CMC 130

Abstract

Almost axisymmetric flows are designed to model tropical cyclones. In 1988, Shutts et al proposed a discrete procedure to construct a solution to the forced axisymmetric flows within a rigid boundary. In this talk, I will discuss how we have extended their results to the continuous case within an appropriate free boundary domain. In addition, I will explain how overcoming an elliptic regularity issue could be an important step toward extending our procedure to handle almost axisymmetric flows.

## Friday, October 12, 2018

Title
Speaker

Time
Place

Universality: from Taylor series to optimal polynomial approximants
Myrto Manolaki
University of Dublin
3:00pm-4:00pm
CMC 130
Catherine Bénéteau

Abstract

It is known that for most analytic functions on the unit disc $$D$$, the partial sums of their Taylor series behave chaotically outside $$D$$, in the sense that they can approximate every plausible function. Analytic functions with such universal Taylor expansions have been intensively studied over the past 20 years. After an overview of the subject, I will discuss the phenomenon of universality in a non-linear setting: namely, for optimal polynomial approximants of reciprocals of analytic functions.

## Friday, October 5, 2018

Title
Speaker

Time
Place

Ring Theoretic Aspects of Quandles
Boris Tsvelikhovskiy
Northeastern University
3:00pm-4:00pm
CMC 130

Abstract

A quandle is a set $$X$$ with a binary operation satisfying axioms analogous to Reidemeister moves (this operation is usually nonassociative). They were introduced independently by Joyce and Matveev in the 1980's with the purpose of constructing invariants of knots. In a recent paper arXiv:1709.03069 the authors initiated the study of quandle rings. For the duration of the talk we will mostly concentrate on finite quandles (the set $$X$$ consists of finitely many elements). After discussing some basic properties of these rings, I will explain how ideas from representation theory of finite groups and semigroups under certain assumptions allow to classify simple right and left ideals. Examples will be provided. In the final part of the talk some open problems will be mentioned.

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Speaker

Time
Place