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Fibonacci and Lucas analogues of binomial coefficients and what they count (Curtis Bennett, CSULB)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number.  For example, the Fibonomial $${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ since the first six Fibonacci […]

On the interplay of functional analysis and operator theory (Puig de Dios, UCR)

Shanahan B460, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982): 1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator; 2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic […]

Models of Biological Tissue Electrostatics and Molecular Transport (Jim Sterling, KGI)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

In this presentation, some fundamentals of electrostatics in biology will be discussed with focus on the fact that most biological macromolecules including nucleic acids, carbohydrates, and proteins are negatively-charged. Electroneutrality requires cations to move toward the macromolecules where they both screen and bind to the negatively-charged groups. An important class of mathematical models of species-flux […]

Matrix multiplication: the hunt for $\omega$ (Mark Huber, CMC)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps.  Only in 1969 did Strassen discover that there was a faster method.  In this talk I'll discuss his finding, how the Master Theorem for divide-and-conquer plays into it, and how it was shown that finding determinants, inverting matrices, […]

A General Bayesian Discrete Time Survival Model (King, CPP)

Shanahan B460, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

Abstract: "We present a general Bayesian statistical model for discrete time, discrete state space stochastic processes. Applications include the modeling of recurrent and episodic disease processes, such as episodes of illicit drug use, as well as social processes such as educational enrollment and employment. We also present Markov chain Monte Carlo inference algorithms for our […]

Geometry of quotient varieties and the algebra of conformal blocks (Han-Bom Moon Fordham University)

Roberts North 104, CMC 320 E. 9th St., Claremont, CA, United States

An important question in classical representation theory is when the tensor product of two irreducible representations has another representation as a factor. In this talk, I will introduce a quantum generalization of this question and explain how we may relate this question to geometry of quotients of certain complex manifolds. This is joint work with […]

GEMS Workshop: “Graphs, matrices, and recurrences” with Professor Lucas Bang, from Harvey Mudd College

Shanahan 1480, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

TOPIC: Graphs, matrices, and recurrences Abstract: In mathematics, we are often surprised to find that problems that look very different are actually the same problem in a different guise! In this seminar, we will build on the previous discussions about graph theory and describe how other areas of math are closely related to graphs. Specifically, […]

Applied Math Talk: Solving Complex Public Health Problems—Cancer, Obesity and Aging (Jessica Dehart, CGU)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Abstract: Remember smoking? What’s the new public health problem? In the US, we are currently entangled within three converging and intertwined complex problems: Cancer, Obesity, Aging. There are over 16 million cancer survivors living in the US as we speak. Over 50% of our society is overweight and/obese. Our society is aging and the age […]

Chow rings of heavy/light Hassett spaces via tropical geometry (Dagan Karp, HMC)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

In this talk, I will try to give a fun introduction to tropical geometry and Hassett spaces, and show how tropical geometry can be used to compute the Chow rings of Hassett spaces combinatorially. This is joint work with Siddarth Kannan and Shiyue Li.

Unravelling Biochemistry Mysteries: Knot Theory Applied to Biochemistry (Price, University of San Diego)

Shanahan B460, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

Abstract: Mathematical modeling is an effective resource for biologists since it provides ways to simplify, study and understand the complex systems common in biology and biochemistry. Many mathematical tools can be applied to biological problems, some traditional and some more novel, all innovative. This presentation will review the mathematical tools that are used to model […]

Enhancements of the quandle coloring invariant for knots (Karina Cho, Harvey Mudd College)

Roberts North 104, CMC 320 E. 9th St., Claremont, CA, United States

Quandles are algebraic structures that play nicely with knots. The multiplicative structure of finite quandles gives us a way to "color" knot diagrams, and the number of such colorings for a given knot and quandle is called the quandle coloring invariant. We strengthen this invariant by examining the relationships between the colorings, which are given […]

Applied Math Talk: Nonlocal problems for linear evolution equations (Prof. Smith David Andrew, Yale-NUS College, Singapore)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral […]