Colloquium

Peter Coffee, VP for Strategic Research, Salesforce

Acquiring Intelligence: Assembling Tomorrow's Data-Driven, AI-Everywhere World

It's been said that AI is the discipline that kicks its successes out of the nest: that once it works, it's called "language processing" or "image recognition" or "predictive recommendation" or some other specific description of the useful result. (Whatever's left behind as AI, it's been said, is what's "Almost Implemented.") Peter Coffee, global VP for Strategic Research at cloud computing leader Salesforce, will be with us once again, this time to discuss the component skills and disciplines that actually are implemented in the company's Einstein machine-intelligence portfolio. He will also share the process of identifying and acquiring the companies and teams that have been assembled into this real-world layer of "Assistive Intelligence" (perhaps a more useful definition of "AI"), across the Salesforce Platform, and to discuss the academic and career preparation that leads toward tomorrow's opportunities.

Monday, Februay 27, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

James Tipton
Visiting Assistant Professor

Infinite Product Representations of Kernel Functions on Fractals

A fractal is, loosely speaking, an image which exhibits a degree of self-similarity. In the early eighties Benoit Mandelbrot published the classic, Fractal Geometry of Nature, in which he argued that many natural phenomena were better modeled by fractals.  The fractals we will consider are obtained through the iteration of quadratics, although the results presented here hold in much greater generality.

Shortly after Mandelbrot's publication, mathematicians began looking for ways to extend various branches of analysis to fractals.  Among these branches is functional analysis, and in particular we will look at a recently developed method for constructing a kernel function on a given fractal.

Uniquely associated to any kernel function is a Hilbert space of functions in which every linear evaluation functional is bounded.  These spaces are called reproducing kernel Hilbert spaces, and as a Hilbert space, notions of length and angle can be defined.  The construction we follow represents the kernel function as an infinite product involving iterations of the quadratic defining the fractal of interest.  We will determine precisely which quadratics this construction holds for.

Monday, March 6, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Katharine Shultis
Gonzaga University

Systems of parameters and the Cohen-Macaulay property

Let \(R\) be a commutative, Noetherian, local ring and \(M\) a finitely generated \(R\)-module. Consider the module of homomorphisms \(\operatorname{Hom}_R(R/\mathfrak{a},M/\mathfrak{b} M)\) where \(\mathfrak{b}\subseteq\mathfrak{a}\) are parameter ideals of \(M\). When \(M=R\) and \(R\) is Cohen-Macaulay, Rees showed that this module of homomorphisms is always isomorphic to \(R/\mathfrak{a}\). Recently, K. Bahmanpour and R. Naghipour showed that if \(\operatorname{Hom}_R(R/\mathfrak{a},R/\mathfrak{b})\) is isomorphic to \(R/\mathfrak{a}\) for every pair of parameter ideals \(\mathfrak{b}\subseteq\mathfrak{a}\) then \(R\) is Cohen-Macaulay. In this talk, we will define the terms above and discuss the structure of \(\operatorname{Hom}_R(R/\mathfrak{a},M/\mathfrak{b}M)\) for general \(R\).

Monday, March 13, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Eric Chesebro
University of Montana

Combinatorial polynomials and the geometry of 2-bridge links

We will discuss a combinatorial family of 1 variable integer polynomials indexed by the rational numbers.  Along the way, we will talk about Fibonacci numbers, Chebyshev polynomials, the Farey graph, and the hyperbolic geometry of 2-bridge links.

Monday, March 27, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Ryan Grady
Montana State University

An intro to quantum BV theory

Starting from elementary differential topology, I will introduce quantum field theory in the Batalin-Vilkovisky (BV) formalism.  I will discuss the relationship between quantum BV theories and projective volume forms.  In particular, I will illustrate (via example) how to build volume forms on interesting moduli spaces using BV theory.

Monday, April 3, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Diana Schepens
Montana State University – PhD Candidate

The effects of metabolite production cost on cooperation in microbial communities

Metabolic cross-feeding between microbes is observed in many microbial communities. It has been experimentally observed that cross-feeding synthetic communities have increased level of fitness and cell growth as compared to wild type cells. There are also numerous examples of cross-feeding communities in nature.

Our goal is to develop a model to analyze the effects that resource investment into metabolite production have on the evolution of syntrophy in a microbial community. We first analyze the investment into the substrates and enzymes that are used to produce the metabolite in a metabolic pathway in order to formulate a representation of the cost of producing the metabolite. We then combine this cost function together with a model of a microbial community containing a variety of phenotypes to observe conditions under which cooperation occurs.

Monday, April 10, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Linh Nguyen
University of Idaho

Mathematics of Photoacoustic Tomography

Photoacoustic tomography (PAT) is a hybrid method of imaging. It combines the high contrast of optical imaging and high resolution of ultrasound imaging. A short pulse of laser light is scanned through the biological object of interest. The photoelastic effect produces an ultrasound pressure propagating throughout the space, which is measured by transducers located on an observation surface. The goal of PAT is to find the initial pressure inside the object, since it contains helpful information of the object.

The mathematical model for PAT is an inverse source problem for the wave equation. In this talk, we will discuss several methods for solving this inverse problem. They include inversion formulas, time reversal techniques, and iterative methods.

Monday, April 17, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Andrew Hoegh
Montana State University

Predictive Spatiotemporal Modeling

Statistical modeling is often used for one of two distinct paradigms: explanatory or predictive inference. Data science or predictive analytics based applications are often concerned with prediction. With an emphasis on methodology for predictive inference in spatiotemporal settings, this talk will provide an overview of a multiscale spatiotemporal framework developed to predict outbreaks of social unrest in Central and South America. Civil unrest is a complicated, multifaceted social phenomenon that is difficult to forecast. Relevant data for predicting future protests consist of a massive set of heterogenous data sources, primarily from social media. A modular approach to extract pertinent information from disparate data sources is implemented to develop a Bayesian multiscale framework to fuse prediction from algorithms mining social media.

Monday, April 24, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

Colloquium

Charlie Katerba
University of Montana – PhD Candidate

From Hyperbolic to Algebraic Geometry through Character Varieties

In this expository lecture, we will review some of the basics of hyperbolic geometry from the perspective of representation theory and use this point of view to motivate the study of a 3-manifold's character variety.  Along the way we will touch on some classic results in low-dimensional topology, explore concrete examples, and discuss various ways to continue applying character varieties to 3-manifold topology.  

This lecture will review the background material for the speaker's dissertation defense.

Monday, May 1, 2017 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109