Saturday, May 2nd 2015, at Bay View Academy in Monterey, CA

Saturday May 2nd 2015, at Bay View Academy, Monterey CA 


The 30th Bay Area Discrete Math Day (BAD Math Day) will take place at Bay View Academy in Monterey, CA on Saturday, May 2nd, 2015. All talks will be held in the MUR.

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BAD Math Days are one-day meetings aimed at facilitating communication between researchers and graduate students of discrete mathematics around the San Francisco Bay Area. These days happen twice a year and strive to create an informal atmosphere to talk about discrete mathematics. The term "discrete mathematics" is chosen to include at least the following topics: Algebraic and Enumerative Combinatorics, Discrete Geometry, Graph Theory, Coding and Design Theory, Combinatorial Aspects of Computational Algebra and Geometry, Combinatorial Optimization, Probabilistic Combinatorics, Combinatorial Aspects of Statistics, and Combinatorics in Mathematical Physics.





Registration

Light breakfast, lunch and dinner will be provided if you register at the bottom of this page by April 22nd, 2015.  Missed this deadline and still considering attending?  Please send email to Ralucca Gera

Schedule

All talks will he held in the MUR at Bay View Academy. 

9:00-10:00amWelcome and refreshments
10:00-10:30amMateusz Michalek, Berkeley
Title: Quantum jumps of normal polytopes
Abstract:
Normal polytopes are combinatorial objects corresponding to embedded normal projective toric varieties. Various
aspects of these polytopes have been studied with tools and inspirations coming from algebra, geometry and
combinatorics. In my talk I would like to present the poset structure on the family of normal polytopes, that
turns out to have very interesting geometry. I will focus on recent results from a joint work with Winfried Bruns
and Joseph Gubeladze providing maximal normal polytopes. I will also present several challenging open problems
10:45-11:15am

Jenny Wilson, Stanford

Title: Representation stability and classical Weyl groups

Abstract:
Over the past several years Church, Ellenberg, Farb, and Nagpal developed a framework for studying sequences of representations of the symmetric groups, using a concept they call an FI--module. I will give an overview of this theory, and describe how it generalizes to representations of the Weyl groups in type B/C and D. This machinery enables us to deduce strong constraints on the pattern of irreducible representations, the characters, and the growth rate of these sequences from an elementary "finite generation" condition. Applications include the diagonal coinvariant algebras associated to the classical Weyl groups, and the cohomology of various families of groups and spaces related to Artin's braid groups.
11:30-12:30pm

Kevin McCurley, Google

On Problem Selection in Mathematics Research 

Abstract:
When I was a graduate student, I had the luck to hear a lecture by Richard Hamming on how to manage a research career in mathematics. It's now 35 years later, and I've been lucky to have a career where I worked in academia, in government, and in industry. Each of these has different value systems, but each of them provide good sources for problems to work on. I'll draw on some examples during my career to illustrate what makes a good problem to work on.

12:30-2:00pmLunch
2:00-
2:30pm
Nora Youngs, Harvey Mudd College
Title: Neural codes and convexity
Abstract:
Neurons in the brain represent stimuli via neural codes -  binary vectors which represent firing patterns.  One important problem confronted by the brain is to infer properties of represented stimulus spaces using only the intrinsic structure of neural codes.  How does the brain do this? To address this question we define the neural ring, an algebraic object that encodes the full combinatorial data of a code. We show how it can be used to extract relevant features, and to give signatures of the code's realizability by convex sets.
2:45-
3:15pm
Apoorva Khare, Stanford
Critical exponents of graphs

Abstract:
We study the set of powers that preserve positive semidefiniteness, when applied entrywise to matrices with structure of zeros prescribed by a graph. This is part of a broad program to study entrywise functions preserving positivity on distinguished submanifolds of the cone. In our main result, we completely classify the powers preserving positivity with respect to all chordal/decomposable graphs. Additionally, we introduce a new graph invariant which we call the "critical exponent". Our results provide natural connections between combinatorics and analysis by relating the discrete sparsity structures of matrices to their spectral properties. The work also has applications in the regularization of covariance/correlation matrices, where entrywise powers are used to separate signal from noise, while minimally modifying the entries of the original matrix. (Based on joint work with D. Guillot and B. Rajaratnam, Stanford.)


3:15-
4:00pm
Coffee break
4:00-
5:00pm
Jan Vondrak, IBM
Yet Another Algorithmic Local Lemma?

Abstract:
Following Moser's discovery of an efficient algorithm for applications of the Lovasz Local Lemma, there has been extensive research on various extensions of this result. We prove a unifying algorithmic local lemma in an abstract setting assuming a "resampling oracle" for each event. We show that the existence of resampling oracles is equivalent to a positive association property similar to the assumptions of the "lopsided local lemma". In particular, efficient resampling oracles can be designed for the known application scenarios of the lopsided local lemma (random permutations, matchings, spanning trees). We present several new algorithmic results in these scenarios.

(joint work with Nick Harvey)



Directions and Parking

Directions to Bay View Academy, are best found by asking Google Maps to direct you to the 222 Casa Verde Way, Monterey, CA 93940.  If you are driving, parking (which is free unless otherwise marked) is available in the main parking lot, as well as on the street. 

 

Organizers and Sponsors

The BAD Math Committee:


    The 30th Bay Area Discrete Mathematics Day is kindly sponsored by D.E. Shaw and Elsevier, and hosted at Bay View Academy. 

      
       

                
    www.elsevier.com/mathematics          
        




              

    BAD Math Day Registration

    Registration is open till April 22nd, 2015.  Light breakfast, lunch and dinner will be provided if you registered by April 22nd, 2015.  Missed this deadline and still considering attending?  Please send email to Ralucca Gera.

                             
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