Colloquium

Totally geodesic submanifolds in Riemannian geometry

03/08/2017 - 4:15pm
03/08/2017 - 5:15pm
Speaker: 
Thomas Murphy (CSU Fullerton)
Abstract: 

One of the main avenues of research in Riemannian geometry has been submanifold geometry, which studies how one manifold "sits" (embeds)  inside another. It is analogous to studying subgroups of a given group. Totally geodesic embeddings are the simplest cases to study, but the problem is fiendishly difficult. I will explain carefully the objects mentioned in the title of talk, outline  the history and importance of the classification problem, and explain some  work in progress with Fred Wilhelm (UCR) concerning their existence in generic settings.

Where: 
Shanahan B460, Harvey Mudd

Repetitivity of patterns in mathematical quasicrystals

03/29/2017 - 4:15pm
03/29/2017 - 5:15pm
Speaker: 
Alan Haynes (Univ. of Houston)
Abstract: 

In this talk we will begin with a brief history of the mathematics of aperiodic tilings of Euclidean space, highlighting their relevance to the theory of physical materials called quasicrystals. Next we will focus on an important collection of point sets, cut and project sets, which provide us with mathematical models for quasicrystals. Cut and project sets have a dynamical description, in terms of return times to certain regions of linear R^d actions on higher dimensional tori. As an example of the utility of this point of view, we will demonstrate how it can be used, in conjunction with input from Diophantine approximation, to classify a subset of `perfectly ordered’ quasicrystals.

Where: 
Shanahan B460, Harvey Mudd

Field committee meeting

01/18/2017 - 4:15pm
01/18/2017 - 5:15pm
Speaker: 
Field Committee meeting (faculty)
Abstract: 

Please come to discuss course offerings and other synergistic items. 

Where: 
Shanahan 3481

Random Matrices with Heavy-Tailed Entries: Tight Mean Estimators and Applications

02/22/2017 - 4:15pm
02/22/2017 - 5:15pm
Speaker: 
Stanislav Minsker (USC)
Abstract: 

Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator (and its modifications) is very sensitive to outliers in the data. As P. Huber wrote in 1964, “...This raises a question which could have been asked already by Gauss, but which was, as far as I know, only raised a few years ago (notably by Tukey): what happens if the true distribution deviates slightly from the assumed normal one? As is now well known, the sample mean then may have a catastrophically bad performance…” Motivated by this question, we develop a new estimator of the (element-wise) mean of a random matrix, which includes covariance estimation problem as a special case. Assuming that the entries of a matrix possess only finite second moment, this new estimator admits sub-Gaussian or sub-exponential concentration around the unknown mean in the operator norm. We will explain key ideas behind our construction, as well as applications to covariance estimation and matrix completion problems. The paper is available online at https://arxiv.org/abs/1605.07129

Where: 
Shanahan B460, Harvey Mudd

Pre-colloquium Non-colloquium Party

08/31/2016 - 4:15pm
08/31/2016 - 5:30pm
Speaker: 
(none)
Abstract: 

The traditional year-opening social event for the Claremont Colleges Mathematics Community, will be held at the Freeberg Forum (Kravis Lower Court 62) at the Claremont McKenna campus. Spouses, partners, and family are welcome. Professor Chiu-Yen Kao (CMC) and Professor Deanna Needell (CMC), Colloquium co-chairs, hope to see everyone there for refreshments and other pleasant pursuits.

 

Where: 
Kravis Center Lower Court 62, Claremont McKenna College

Sensing and Decision-Making in Animal Search

02/08/2017 - 4:15pm
02/08/2017 - 5:15pm
Speaker: 
Scott McKinley (Tulane)
Abstract: 
Due to the rapid growth of animal movement data obtained by GPS, radio tracking collars and other means, there is a growing recognition that classical models of encounter rates among animal populations should be revisited. Recent theoretical investigations have demonstrated that biologically relevant modifications to classical assumptions about individual behavior can bring about non-trivial changes in the formulation of population-scale dynamical systems. Put more simply: a panther does not move around like a Brownian motion, but PDEs used in Mathematical Ecology pretend like they do!
 
The first paradigm shift in describing animal movement was to move towards “Levy Flight” models that take into account the tendency of searching animals to make long excursions. The problem with this theory is that animal decisions are hypothesized to be divorced from stimuli in their environment. In this talk, I will review some of the conventional wisdom that supports the Levy flight theory, but through a few examples, I will make the case that animal movement patterns should not be separated from the spatial environmental features that shape them. In fact, animal sensing and decision-making are “leading-order” effects in observed data, and their study gives rise to new ecological observations and novel mathematical challenges.
Where: 
Shanahan B460, Harvey Mudd

Delay in the System: Oscillations caused by non-trivial response time

11/30/2016 - 4:15pm
11/30/2016 - 5:15pm
Speaker: 
Lauren Lazarus (HMC)
Abstract: 

Delayed terms in differential equations are frequently considered for their representation of information travel time or other physical effects between members of a system.  Interesting behaviors also occur when an individual unit has internal delay, implying information processing and response time.  In both cases, the delay may affect the resonance and synchronization behavior of the system.

I will introduce a model of an oscillator whose periodic motion is solely caused by its internal delay.    We will use perturbation methods to investigate how this model reacts to different styles of coupling and forcing.  In these contexts, we explore similarities and differences in behavior between this model and the traditional ODE oscillator models.

 

Where: 
Kravis Center Lower Court 62, Claremont McKenna College

Finding Shape in Data

10/12/2016 - 4:15pm
10/12/2016 - 5:15pm
Speaker: 
Brittany Fasy (Montana St.U.)
Abstract: 

Topology studies the structure of shapes. Topological data analysis (TDA) is the

study of the shape of (large, high-dimensional, and noisy) data. Often, in
TDA, the data set is transformed into a concise descriptor, such as a
persistence diagram or a dendogram, which can then be used to (indirectly)
compare or classify the data sets. In this talk, we will define a persistence
diagram and confidence sets for persistence diagrams. Then, we will discuss how
we can use these confidence sets to perform statistical hypothesis testing, and
provide a few examples of where we've applied (or are applying) these methods.
The examples will include road network analysis, prostate cancer diagnosis, and the study of matter throughout the universe.

 

Where: 
Kravis Center Lower Court 62, Claremont McKenna College

Knotting and linking in spatial graph embeddings

12/07/2016 - 4:15pm
12/07/2016 - 5:15pm
Speaker: 
Kenji Kozai (HMC)
Abstract: 

An abstract graph can be realized (embedded) in 3-dimensional space by associating vertices to a point in space and edges between vertices as an arc between the associated points. A given graph has infinitely many embeddings, and some embeddings may be more complicated than others. One way of measuring how complicated an embedding is is to consider the knotting and linking of cycles in the graph embedding. I will give an introduction to some elementary knot and link invariants, and then show how they can be used to prove that certain graphs are intrinsically linked or knotted, that is every embedding has a non-trivial link or knot. In addition, I will discuss random knot and graph embedding models as well as what can be said about "typical" embedding of graphs.

Where: 
Kravis Lower Court, Claremont McKenna College

Much Ado About Knot Things

10/05/2016 - 6:05am
10/05/2016 - 7:05am
Speaker: 
Matt Rathbun (Cal State Fullerton)
Abstract: 

This talk will give a brief introduction to knot theory, and some of the applications to understanding the behaviors and mechanisms of DNA and interactions with proteins. No background will be assumed.

Where: 
Kravis Center Lower Court 62, Claremont McKenna College
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