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Mathematics & Statistics
Colloquium Archive

# Colloquia — Spring 2017

## Friday, April 21, 2017

Title
Speaker

Time
Place

TBA
Felix Lazebnik
University of Delaware
3:00pm-4:00pm
CMC 204
Xiang-dong Hou

Abstract

TBA

## Friday, April 14, 2017

Title
Speaker

Time
Place

TBA
University of Pennsylvania
3:00pm-4:00pm
CMC 204
Nataša Jonoska

Abstract

TBA

## Friday, April 7, 2017

Title
Speaker

Time
Place

TBA
Michael S. Jolly
Indiana University
3:00pm-4:00pm
CMC 204
Yuncheng You

Abstract

TBA

## Friday, March 31, 2017

Title
Speaker

Time
Place

TBA
Yili Hong
Department of Statistics
Virginia Tech
3:00pm-4:00pm
CMC 204
Lu Lu

Abstract

TBA

## Friday, March 24, 2017

Title
Speaker

Time
Place

TBA
Stéphane Lafortune
College of Charleston
3:00pm-4:00pm
CMC 204
Wen-Xiu Ma

Abstract

TBA

## Friday, March 10, 2017

Title
Speaker

Time
Place

TBA
Dimitris Giannakis
Courant Institute of Mathematical Sciences
3:00pm-4:00pm
CMC 204
Jing Tian

Abstract

TBA

## Friday, March 3, 2017

Title
Speaker

Time
Place

TBA
Yuri Gurevich
Microsoft Research
Redmond, WA
3:00pm-4:00pm
CMC 204
Greg McColm

Abstract

TBA

## Friday, February 3, 2017

Title
Speaker

Time
Place

Wavelet Modeling: All That Scaling
Branislav Vidakovic
Georgia Institute of Technology
3:00pm-4:00pm
CMC 204
K. M. Ramachandran

Abstract

In this overview talk we focus on the wavelet-based estimation of scaling indices of self-similar time series and images. This estimation is conducted in multiscale domains. We consider a range of wavelet and wavelet-like decompositions: orthogonal, nondecimated, wavelet packets, complex-number decompositions, autocorrelation shells of wavelets, and spherical wavelets. They all result in a hierarchy of imbedded multiresolution subspaces that could produce a valid multiscale spectra. Like in the Fourier transforms where the linear decay of the log-power spectra over the frequencies characterizes the regularity/smoothness of a time series/image, the decay of the log-average squared wavelet coefficients leads to an alternative and arguably more local and stable measure of signal/image regularity. We provide examples from medicine, finance, and geosciences in which the scaling indices turn out to be useful in tasks of statistical learning. In the talk we also overview some traditional results, some results from the past research of the speaker and his collaborators, as well as some interesting results from the ongoing research. We will point out at several interesting avenues for possible future research.

## Friday, January 27, 2017

Title
Speaker

Time
Place

Automaton groups and square complexes
Ievgen Bondarenko
Taras Shevchenko National University of Kyiv
Kyiv, Ukraine
3:00pm-4:00pm
CMC 204
Dmytro Savchuk

Abstract

Any automaton-transducer gives rise to a square complex: one can take a unit square with labeled and oriented edges for each arrow in automaton and glue these squares to get a complex. Transitions in automaton correspond to relations in the fundamental group of the associated square complex. In this talk, based on a joint work with Bohdan Kivva, I will discuss the connection between groups generated by automata, tiling properties of associated collection of squares, and residual properties of the fundamental groups of these square complexes. In particular, I will show how to construct square complexes with non-residually finite $$\mathrm{CAT}(0)$$ fundamental group from any bireversible automaton with infinite automaton group.

## Friday, January 20, 2017

Title
Speaker

Time
Place

On Vassiliev Invariants for Knots in the Solid Torus
Khaled T. Bataineh
Jordan University of Science and Technology
3:00pm-4:00pm
CMC 204
Mustafa Hajij

Abstract

Vassiliev invariants (or finite type invariants), discovered around 1989, provided a new way of looking at knots. A Vassiliev invariant of order $$m$$ is a knot invariant that can be extended (in a precise manner) to an invariant of certain singular knots that vanishes on singular knots with $$m+1$$ singularities and does not vanish on some singular knot with '$$m$$' singularities.

Michael Polyak and Oleg Viro gave a description of the first nontrivial invariants of orders 2 and 3 for knots in the Euclidean space by means of Gauss diagrams. We give our description of the infinite families of Vassiliev invariants of orders 1 and 2 for knots in the solid torus with zero winding number.

For the order 1 invariants we give two ways of describing these invariants. One of them uses decorated Gauss diagrams, and the other uses techniques of lifting the solid torus into its universal cover and applying linking numbers.

For the order 2 invariants we introduce a natural filtration in the space of knots and singular knots in the solid torus, and start the study of the Vassiliev invariants of order 2 with respect to this filtration. The main result states that any such invariant within the second term of this filtration in the space of knots with zero winding number is a linear combination of seven explicitly described decorated Gauss diagram invariants. This introduces a basis (and a universal invariant) for the Vassiliev invariants of order 2 in the second term. Then we formalize the problem of exploring the set of all invariants of order 2 for knots with zero winding number.

Title
Speaker

Time
Place