The 29th Bay Area Discrete Math Day (BAD Math Day) will take place at Stanford University on Saturday, September 27, 2014. All talks will be held in the Sloane Mathematics Center (as seen on this campus map
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.
Lunch will be provided if you register at the bottom of this page by September 19th. Missed this deadline and still considering attending? Please send email to Angela Hicks.
All talks will he held in Sloane Mathematics Center.
||Welcome and refreshments
San Jose State University
|Goodness-of-fit testing for network models
Social networks and other large sparse data sets pose significant challenges for statistical inference, as many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic statistics offers an approach to goodness-of-fit testing for log-linear network models that relies on the theory of Markov bases and is intimately connected with the geometry of the model as described by its fibers.
Most current practices require the computation of the entire Markov basis, which is infeasible in many practical settings. In this talk, we present a dynamic procedure to explore the fibers of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of the model.
We demonstrate the approach on the Holland-Leinhardt $p_1$ model for random directed graphs that allows for reciprocated edges. This is joint work with Petrović and Despina Stasi.
San Francisco State University
|Exotic spectra of fractal measures
A probability measure is called a spectral measure if we can find some collection of exponential orthonormal basis in it L^2 space. The
frequency set will be called a spectrum for the measure. It was found that fractal singular measures could also be spectral. Its spectra carry a lot of exotic structure and is related to tiling of integers. In this talk, we will give a brief introduction and present some of the recent progress.
University of California-San Diego
|Gaps in eigenfunctions of Graphs
We will examine the gaps and stretches in eigenfunctions in connection with the Cheeger inequalities and Harnack inequalities.
University of California-Davis
|Pattern-avoiding permutations and Brownian excursion
Dyck Paths of length 2n and permutations on [n] that avoid a pattern of length three are both counted by the Catalan numbers. Naturally there exists bijections between the two sets. Remarkably, given the right choice of bijection, both of these random objects converge (in some sense) to the same thing, Brownian excursion. This connection to Brownian excursion helps answer all sorts of questions about the permutations. More importantly the connection leads to many new questions. This is joint work with Christopher Hoffman and Douglas Rizzolo.
|From 2-periodic functors in the category of Soergel bimodules
to q-analogues of Chebyshev polynomials via the Metropolis algorithm
Let W be a Coxeter group and let H(q) be its Iwahori-Hecke algebra. For each involution * of W, there exists a certain H(q)-module M,
recently studied by Lusztig and Vogan, with a basis given by the *-twisted involutions in W. The action of the standard generators of H(q) on one simple basis of M describes a Markov chain on the set of twisted involutions in W. When W is finite, this Markov chain has a
stationary distribution in which the probability of being at a given element is equal to a simple function of the length divided by a
certain normalizing constant L_W(q). This normalizing constant may be interpreted as an analogue of the Poincare series for twisted
involutions, and is well-defined for any Coxeter group. When studying L_W(q) for affine Weyl groups, it is natural to introduce a certain
bivariate generalization T_W(x,q), which reduces to L_W(q) on setting x=1. Remarkably, in type A the generalized series T_W(x,q) gives a
q-analogue of the Chebyshev polynomials of the first kind. Even more surprisingly, these q-analogues have previously appeared in recent
work of Cigler, in an entirely unrelated context. This is joint work with Megan Bernstein and Graham White.
Universitaet Marburg, Germany
|Associahedra and initial ideals of classical ideals
We give a survey on work over the last ten years that relates
initial ideals of classical ideals (such as determinantal,
Pfaffian, Plücker relations, etc.) and various generalizations of
Directions to Stanford University are best found by asking Google Maps to direct you to the Stanford Oval. If you are driving, parking (which is free on weekends unless otherwise marked) is available in a number of places on campus. The closest spaces to the math department are around the oval, but you can find a number of 'A' and 'C' spaces marked on this map. Note that most spaces are not particularly close to the department, so plan some time to walk from your car.
The 28th Bay Area Discrete Mathematics Day
is kindly sponsored by Stanford University's Mathematics Research Center, D.E. Shaw, and Elsevier.
It is possible to take public transit to Stanford University, but be aware that the nearest stops to Stanford on a Saturday morning (including the nearest Caltrain station) are approximately a mile from the mathematics department. If you need a ride, or if you are able to give
rides, please contact your local member of the BAD Math Committee or let us know below.
The BAD Math Committee:
- Federico Ardila, San Francisco
- Yan Zhang, University of
- Tim Hsu, San Jose State University
- Carol Meyers, Lawrence Livermore
- Angela Hicks, Stanford University
Scott, Santa Clara University
Slofstra, University of California, Davis
- Ellen Veomett, Saint Mary's College
- Ralucca Gera, Naval Postgraduate School
Registration is closed. Lunch will be provided if you
registered by September 19th. Missed this deadline and still considering attending? Please send email to Angela Hicks.