__Claremont Graduate University__ | __Claremont McKenna__ | __Harvey Mudd__ | __Pitzer__ | __Pomona__ | __Scripps__

Proudly Serving Math Community at the Claremont Colleges Since 2007

Copyright © 2011 Claremont Center for the Mathematical Sciences

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

11/26/2014 - 12:00am

Speaker:

N/A

Abstract:

TBA

Where:

n/a

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

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

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 with << non-zero entries) to efficiently reconstruct it from very few (say , where < << ) 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 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

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

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

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

10/08/2014 - 4:15pm

10/08/2014 - 5:15pm

Speaker:

Gary Rosen, University of Southern California

Abstract:

We have formulated a mathematical model for the trans-dermal excretion and measurement of alcohol as part of an ongoing effort to develop a functional integrated trans-dermal alcohol biosensor (TAS) and data analysis system. The TAS system, which measures the alcohol content in perspi- ration has the potential to non-invasively, unobtrusively and accurately determine blood alcohol concentration (BAC) over both short (minutes) and long (hours, days, weeks) periods in the clinic and in the field and to provide useful alcohol related physiological and behavioral information for researchers, clinicians and forensic applications. The problem of obtaining BAC from TAS mea- sured trans-dermal alcohol concentration (TAC) is fundamentally an ill-posed inverse problem. If one thinks of the dynamics of the trans-dermal transport process as a black box with input BAC and output TAC, the problem of determining BAC from the TAC signal becomes one of inverting the transformation represented by the black box. Developing clinical software that will accurately and efficiently carry out this inversion is fundamentally a mathematical problem. In this talk we discuss how this problem can be modeled and analyzed.

Where:

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

10/01/2014 - 4:15pm

10/01/2014 - 5:15pm

Speaker:

David Bachman, Pitzer College

Abstract:

With the invention of 3D printing, mathematics has been transformed from abstract ideas that can only be sketched on a blackboard, to physical objects that you can hold in your hand. In this talk we'll see how to go from an idea of some shape, to a mathematical model, and finally to a physical object. A 3D printer will be on hand to see in action.

Where:

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