USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

(Leader:

**Title**

**Speaker**

**Time**

**Place**

TBA

Daviel Leyva

2:00pm-2:50pm

CMC 108

**Abstract**

TBA

**Title**

**Speaker**

**Time**

**Place**

TBA

TBA

2:00pm-2:50pm

CMC 108

**Abstract**

TBA

Veteran's Day Holiday -- no seminar this week.

**Title**

**Speaker**

**Time**

**Place**

TBA

TBA

2:00pm-2:50pm

CMC 108

**Abstract**

TBA

**Title**

**Speaker**

**Time**

**Place**

TBA

TBA

2:00pm-2:50pm

CMC 108

**Abstract**

TBA

**Title**

**Speaker**

**Time**

**Place**

TBA

TBA

2:00pm-2:50pm

CMC 108

**Abstract**

TBA

**Title**

**Speaker**

**Time**

**Place**

Spaces of Geometric Graphs

Greg McColm

2:00pm-2:50pm

CMC 108

**Abstract**

A *geometric graph* is a graph embedded in some (nice) geometric space; usually a Euclidean space. A geometric graph may be generated from a putative quotient graph with some matrix groups assigned to the quotient graph's vertices and vectors (and perhaps matrices) assigned to the edges. If we treat the matrices as constants and the vectors as variables, we obtain an ensemble of geometric graphs parametrized by a vector space of input values.

**Title**

**Speaker**

**Time**

**Place**

Covering and Navigating Geometric Graphs

Greg McColm

2:00pm-2:50pm

CMC 108

**Abstract**

A *geometric graph* is a graph embedded in some (nice) geometric space; usually a Euclidean space. Given a group acting on that Euclidean space, the symmetry group \(S\) of a graph \(\Gamma\) embedded in that space is the group of automorphisms of \(\Gamma\) induced by the group acting on the underlying space. This symmetry group does not necessarily act freely on \(\Gamma\), and yet we would like to “lift&rdqup; \(\Gamma\) from \(\Gamma/S\). We describe a method for doing so, and en route, we obtain a method for parametrizing classes of periodic (and other very regular) geometric graphs.

**Title**

**Speaker**

**Time**

**Place**

Graph Covers, Quotients, Lifts, and Immersion

Greg McColm

2:00pm-2:50pm

CMC 108

**Abstract**

Given a graph \(\Delta\), a covering graph of \(\Delta\) is a graph \(\Gamma\) such that there is a homomorphism \(\phi\) from \(\Gamma\) to \(\Delta\) that is bijective from neighborhood to neighborhood. Connected covering graphs of connected graphs can be determined up to isomorphism by “lifting” walks on the covered walk up to vertices of the covering graph. We adapt this theory to the problem of generating a graph from its quotient graph and generators of its group.

**Title**

**Speaker**

**Time**

**Place**

Graphs made of forms

Greg McColm

2:00pm-2:50pm

CMC 108

**Abstract**

Metric spaces of finite and infinite geometric graphs of high symmetry can be described using linear forms. Given an abstract graph composed of forms, we obtain an ensemble of homomorphic images of that graph embedded in Euclidean space. We look at some fundamentals concerning these abstract graphs and the spaces of graphs that they characterize.

**Title**

**Speaker**

**Time**

**Place**

Gromov-Monge Quasimetrics and Distance Distributions

Tom Needham

Ohio State University

2:00pm-2:50pm

CMC 108

**Abstract**

In applications in computer graphics and computational anatomy, one seeks measure-preserving maps between shapes which preserve geometry as much as possible. Inspired by this, we define a distance between arbitrary compact metric measure spaces by blending the Monge formulation of optimal transport with the Gromov-Hausdorff construction. We show that the resulting distance is an extended quasi-metric on the space of compact mm-spaces, which has convenient lower bounds defined in terms of distance distributions. We provide rigorous results on the effectiveness of these lower bounds when restricted to simple classes of \(mm\)-spaces such as metric graphs or plane curves. This is joint work with Facundo Mémoli.

**Topic**

**Speaker**

**Time**

**Place**

Quasigroups and their application in several applied areas

Danilo Gligoroski

Norwegian University of Science and Technology

Trondheim, Norway

2:00pm-2:50pm

CMC 108

**Abstract**

In the talk, I will briefly define the algebraic structure quasigroup and quasigroup string transformations and their related combinatorial structures Latin Squares. Then I will show several applications of quasigroups in Cryptography, Coding Theory, Computer Science and 5G. In cryptography quasigroups have been used in primitives such as block ciphers, stream ciphers, hash functions and authenticated ciphers. Popular modes of operations of block ciphers such as CBC, OFB and CTR are actually quasigroup string transformations. I will show how can we use Latin rectangles to define balanced matrices that can be used in coding theory to define efficient erasure codes. Orthogonal matrices over finite fields are very useful mathematical objects in different areas of computer science since by their use we do not need to spend expensive time to compute their inverses, nor to spend space to store their inverses. I will show how can we use Latin rectangles to efficiently define orthogonal matrices over finite fields. Finally I will show how can we use Latin squares and partial Latin squares for one emerging scientific area: Network slicing in the upcoming 5G networks.