Colloquium

CCMS Field Meeting

01/21/2015 - 4:15pm
01/21/2015 - 5:15pm
Speaker: 
N/A
Abstract: 

TBA

Where: 
Sprague Building, 3rd Floor, HMC

Student Research Poster Session

09/17/2014 - 4:15pm
09/17/2014 - 5:15pm
Speaker: 
Multiple
Abstract: 

This summer, Claremont students in mathematics participated in research projects at the Claremont Colleges as well as at many top universities in North America. Join us in celebrating the efforts of these students by participating in an afternoon of mathematical science and discussion.

Where: 
Shanahan Center for Teaching and Learning (SCTL), at Harvey Mudd, Gallery Basement Space

Geometry without Points

12/03/2014 - 4:15pm
12/03/2014 - 5:15pm
Speaker: 
Dana Scott, Carnegie Mellon University
Abstract: 

Ever since the compilers of Euclid’s Elements gave the “definitions” that “a point is that which has no part” and “a line is breadthless length”, philosophers and mathematicians have worried that the basic concepts of geometry are too abstract and too idealized. In the 20th century writers such as Husserl, Lesniewski, Whitehead, Tarski, Blumenthal, and von Neumann have proposed “pointless” approaches. A problem more recent authors have emphasized is that there are difficulties in having a rich theory of a part-whole relationship without atoms and providing both size and geometric dimension as part of the theory. A solution will be proposed using the Boolean algebra of measurable sets modulo null sets along with relations derived from the group of rigid motions in Euclidean n- space. (Joint work with Tamar Lando, Columbia University.).

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

No Colloquium--Thanksgiving Break

11/26/2014 - 12:00am
Speaker: 
N/A
Abstract: 

TBA

Where: 
n/a

The neural ring: using algebraic geometry to analyze neural codes

11/19/2014 - 4:15pm
11/19/2014 - 5:15pm
Speaker: 
Nora Youngs, Harvey Mudd College
Abstract: 

 Neurons in the brain represent external stimuli via neural codes.   These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field.  An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code.  How does the brain do this?  To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes.  This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the full combinatorial data of a neural code.  We find that these objects can be expressed in a "canonical form'' that directly translates to a minimal description of the receptive field structure intrinsic to the neural code. We analyze the algebraic properties of maps between these objects induced by natural maps between codes.  We also find connections to Stanley-Reisner rings, and use ideas similar to those in the theory of monomial ideals to obtain an algorithm for computing the canonical form associated to any neural code, providing the groundwork for inferring stimulus space features from neural activity alone.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

The Mathematics behind Bar Codes

11/12/2014 - 4:15pm
11/12/2014 - 5:15pm
Speaker: 
Fadil Santosa, IMA, UMN
Abstract: 

Bar codes are ubiquitous–they are used to identify products in stores, parts in a warehouse, and books in a library, etc. In this talk, the speaker will describe how information is encoded in a bar code and how it is read by a scanner. The presentation will go over how the decoding process, from scanner signal to coded information, can be formulated as an inverse problem. The inverse problem involves finding the “word” hidden in the signal. What makes this inverse problem, and the approach to solve it, somewhat unusual is that the unknown has a finite number of states.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

Compressed sensing with support information

11/05/2014 - 4:15pm
11/05/2014 - 5:15pm
Speaker: 
Rayan Saab, University of California, San Diego
Abstract: 

Compressed sensing is a signal acquisition paradigm that utilizes the sparsity of a signal (a vector in $ \mathbb{R}^N $ with $ s $ << $ N $ non-zero entries) to efficiently reconstruct it from very few (say $ m $, where $ s $ <$ m $ << $ N $) generalized linear measurements. These measurements often take the form of inner products with random vectors drawn from appropriate distributions, and the reconstruction is typically done using convex optimization algorithms or computationally efficient greedy algorithms.

We discuss compressed sensing under the additional, and often practical, assumption that we have some estimate of the support-albeit this estimate is not fully accurate.
In this setting, we discuss using weighted $ \ell_1 $ minimization as a reconstruction method. We give reconstruction guarantees that improve on the standard results when the support information is accurate enough and when the weights are chosen correctly.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

Topological Tools for the Real World

10/29/2014 - 4:15pm
10/29/2014 - 5:15pm
Speaker: 
Jean-Luc Thiffeault, University of Wisconsin, Madison
Abstract: 

Topology is emerging as an important new tool for understanding our world. Computational homology, for example, has become standard for analyzing the connectivity of large-dimensional data sets. Here I present another approach, which is more dynamical in nature. The trajectories of ‘particles, whether oceanic floats or people, can be regarded as mathematical objects called braids. By using traditional concepts from topological dynamics, such as topological entropy, we gain insight into the inherent complexity of motion.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

Cutting up Spaces

10/22/2014 - 4:15pm
10/22/2014 - 5:15pm
Speaker: 
Matthew Stamps, KTH Royal Institute of Technology
Abstract: 

At a party, one of Jane’s friends cuts a pizza into 10 pieces using 4 straight cuts such that each pair of cuts intersect somewhere in the interior of the pizza. Without seeing the pizza Jane says “Hmm three of the cuts must have gone through a single point.” How did she come to this conclusion? Come to my talk and find out! I’ll present a whole collection of problems centered around spaces which have been cut up by others.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

Voting in Agreeable Societies

10/15/2014 - 4:15pm
10/15/2014 - 5:15pm
Speaker: 
Francis Su, Harvey Mudd College
Abstract: 

When does a majority exist? How does the geometry of the political spectrum influence the outcome? What does mathematics have to say about how people behave? When mathematical objects have a social interpretation, the associated results have social applications. We will show how math can be used to model people’s preferences and classical results about convex sets can be used in the analysis of voting in “agreeable” societies. This talk also features a research with undergraduates, as well as with HMC President Maria Klawe.

Where: 
Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College
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