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 oneday 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
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.
9:0010:00am 
Welcome and refreshments 
10:0010:30am 
Elizabeth Gross
San Jose State University 
Goodnessoffit 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 goodnessoffit testing for loglinear 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 HollandLeinhardt $p_1$ model for random directed graphs that allows for reciprocated edges. This is joint work with Petrović and Despina Stasi.

10:4511:15am 
ChunKit Lai
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. 
11:3012:30pm 
Fan Chung
University of CaliforniaSan Diego 
Gaps in eigenfunctions of Graphs
We will examine the gaps and stretches in eigenfunctions in connection with the Cheeger inequalities and Harnack inequalities. 
12:302:00pm 
Lunch

2:00
2:30pm 
Erik Slivken
University of CaliforniaDavis 
Patternavoiding 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. 
2:45
3:15pm 
Eric Marberg
Stanford University 
From 2periodic functors in the category of Soergel bimodules
to qanalogues of Chebyshev polynomials via the Metropolis algorithm
Let W be a Coxeter group and let H(q) be its IwahoriHecke 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 welldefined 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
qanalogue of the Chebyshev polynomials of the first kind. Even more surprisingly, these qanalogues have previously appeared in recent
work of Cigler, in an entirely unrelated context. This is joint work with Megan Bernstein and Graham White. 
3:15
4:00pm 
Coffee break 
4:00
5:00pm 
Volkmar Welker
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
the associahedron. 


Directions
and Parking
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.
Carpooling
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.
Organizers
and Sponsors
The BAD Math Committee:
 Federico Ardila, San Francisco
State University
 Yan Zhang, University of
California, Berkeley
 Tim Hsu, San Jose State University
 Carol Meyers, Lawrence Livermore
National Laboratory
 Angela Hicks, Stanford University
 Rick
Scott, Santa Clara University
 William
Slofstra, University of California, Davis
 Ellen Veomett, Saint Mary's College
of California
 Ralucca Gera, Naval Postgraduate School
The 28th Bay Area Discrete Mathematics Day
is kindly sponsored by Stanford University's Mathematics Research Center, D.E. Shaw, and Elsevier.
BAD
Math Day
Registration
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.

