Colloquium

TBA: Calculus of Stem Cells

09/27/2017 - 4:15pm
09/27/2017 - 5:15pm
Speaker: 
Natalia Komarova (UCI)
Abstract: 

TBA

Where: 
Argue Auditorium, Millikan, Pomona College

TBA: Stochastic Homogenization of Reaction-Diffusion Equation

09/06/2017 - 4:15pm
09/06/2017 - 5:15pm
Speaker: 
Andrej Zlatos (UCSD)
Abstract: 

TBA

Where: 
Argue Auditorium, Millikan, Pomona College

Student Poster Session

09/13/2017 - 4:15pm
09/13/2017 - 5:15pm
Speaker: 
Students of the Claremont Colleges
Abstract: 

TBA

Where: 
Millikan Courtyard, Pomona College

TBA: Cassini Mission

11/01/2017 - 4:15pm
11/01/2017 - 5:15pm
Speaker: 
Earl Maize (Jet Propulsion Lab, NASA)
Abstract: 

TBA

Where: 
Argue Auditorium, Millikan, Pomona College

An Afternoon With Euler

02/14/2018 - 4:15pm
02/14/2018 - 5:15pm
Speaker: 
Bill Dunham (Bryn Mawr College)
Abstract: 

Among the greatest of mathematicians is Leonhard Euler (1707-1783), whose insight, industry, and ingenuity are unsurpassed in the long history of mathematics. In this talk we sketch Euler’s life, describe the quantity and quality of his mathematical output, and discuss a few of his discoveries from the realms of number theory, geometry, analysis, and combinatorics.

We then look at a specific theorem: his proof, using integral calculus (!), of what is known as "Euler's Identity" -i.e., exp(ix)=cos(x)+isin(x). We should thereby get a sense of Euler’s genius and see why he is rightly known as “the Master of Us All.”

NOTE: This talk should be accessible to any student who has seen calculus.

Where: 
TBA

High Moments of L-functions

04/26/2017 - 4:15pm
04/26/2017 - 5:15pm
Speaker: 
E. Mehmet Kiral (TAMU, MSRI)
Abstract: 
This talk will cover bounding on sums of powers of L-functions at the center of the critical strip, such as the Riemann Zeta function, Dirichlet L-functions, and L-functions of modular forms. Historical background and the questions related to the Riemann and the Lindelof Hypotheses will be provided.
Where: 
Shanahan B460, Harvey Mudd College

Canonical bases and related structures

03/01/2017 - 4:15pm
03/01/2017 - 5:15pm
Speaker: 
Jacob Greenstein (UC Riverside)
Abstract: 

Canonical bases first appeared as Kazhdan-Lusztig bases in the study of Hecke 
algebras which can be thought of as "q-deformations" of symmetric groups (or, 
more generally, Coxeter groups). These are distinguished bases of an algebra 
with prescribed invariance properties when q is replaced by its inverse. They 
are also triangular with respect to some natural initial basis. Such bases 
play an important role in algebra since Lusztig constructed them in quantum 
groups in early 90-ies using geometric methods. 

Where: 
Shanahan B460, Harvey Mudd College

Biquasiles and Dual Graph Diagrams

01/25/2017 - 4:15pm
01/25/2017 - 5:15pm
Speaker: 
Sam Nelson
Abstract: 

Dual graph diagrams are an alternate way to present oriented knots and links in $R^3$. In this talk we will see how to turn dual graph Reidemeister moves into an algebraic structure known as biquasiles and use this structure to define new integer-valued counting invariants of oriented knots and links.

 

Where: 
Shanahan B460, Harvey Mudd College

Saving California Newts Two Models at a Time

03/22/2017 - 4:15pm
03/22/2017 - 5:15pm
Speaker: 
Courtney Davis (Pepperdine University)
Abstract: 
Santa Monica Mountain (SMM) streams are home to the California newt (Taricha torosa), a species of special concern in California.  Our historically severe drought as well as stream invasion by nonnative crayfish (Procambarus clarkii) that prey upon newt eggs have decimated local newt reproduction.  This has led to localized newt extinctions in some SMM streams.  Restorative measures are currently underway in some SMM streams to remove crayfish through trapping in order to prevent or slow the decline of native species.
 
In collaboration with biologists and undergraduate mathematics students, we have created discrete mathematical models to study the population dynamics of the California newt under drought and crayfish predation.  In this talk, I will describe how we construct two nonlinear systems of discrete equations that include demographic parameters such as survival rates for newt life stages and egg production, which depend upon habitat availability and rainfall. We estimate these demographic parameters using 15 years of stream survey data collected from SMM streams.  Our models capture the observed decline of the studied newt population and replicate crayfish trapping data.  Our drought model makes predictions about how the length and severity of drought can affect the likelihood of persistence and the time to critical endangerment of a newt population.  With our crayfish trapping model, we evaluate the persistence or the time to extinction for newt populations under crayfish trapping regimes when varying the quantity of trapping resources, frequency of trapping implementation, and susceptibility of the crayfish population to trapping. Predictions made with both models inform restorative efforts and crayfish management.

 

Where: 
Shanahan B460, Harvey Mudd College

Planar Algebras: Calculating with Pictures

04/19/2017 - 4:15pm
04/19/2017 - 5:15pm
Speaker: 
James Tener (UCSB)
Abstract: 

Planar algebras were first introduced in the late 90's by Vaughan Jones as an axiomatization of the standard invariant of a subfactor. Jones' idea was that the structure of standard invariants had a description in terms of planar diagrams, and that one could compute things about the subfactor by manipulating the pictures. Since then, planar algebras have been used extensively as a framework for performing rigorous calculations by manipulating diagrams. In this talk I will give an example-driven introduction to planar algebras and diagrammatic calculation, and demonstrate some of the features of working with pictures. If time permits, I will also discuss the state of the on-going project to classify `small' planar algebras, as well as the role played by planar algebras in constructive quantum field theory.

 

 

Where: 
Beckman B460, Harvey Mudd College
Add to calendar
Syndicate content