Welcome to RepTile

A conference on representation theory and tilings
UGA, February 22-24, 2019

• Friday3-? Coverdell S175 Eduard Duryev & Leonid Monin
  Eigengons abstract± How can one visualize algebraic curves given by equations? Consider a polygon in the complex plane with parallel equal sides identified by translations. Complex structure of the plane descends to give a Riemann surface, hence an algebraic curve. But how one identifies which algebraic curve it is? Usually this question is impossible to answer. In our talk we will give a series of examples of such polygons together with the equations of algebraic curves that they define.
• Friday4:30-? Coverdell S175 Peter Smillie & Philip Engel
  Penrose tilings of compact surfaces, Part 1 abstract±    I'll give a few approaches to constructing tilings of compact surfaces by rhombuses glued according to Penrose's matching rules. I'll then give some bounds--a logarithmic lower bound and a polynomial upper bound -- for the growth of the function F_g(n) which gives the number of Penrose tilings of a genus g surface with n tiles.
• Friday 6:30-? 555 Morton Dinner at Phil's Place
  Bring food and wine abstract± We will discuss amazing things at this dinner. It will be awesome, which is why you should come.
• Saturday9-10 Coverdell S175 Coffee & Bagels
  Brought to you from ABC abstract±    (Athens Bagel Company)
• Saturday 10-? CoverdellS175 Leonid Monin
  Counting geodesics on hyperbolic surfaces abstract±
• Saturday 11:15-? CoverdellS175 Eduard Duryev
  Square-tiled surfaces and Hurwitz spaces of branched covers abstract±
• Saturday 12:30-? 1427 Lumpkin Lunch
  Cali & Tito's abstract± You put food in your mouth and chew.
• Saturday 2:30-? CoverdellS175 Peter Smillie
  Penrose tilings of compact surfaces, Part 2 abstract±
• Saturday 4-? CoverdellS175 Ben Dozier
  Affine measures and short saddle connections abstract± A stratum of translation surfaces comes equipped with a natural Lebesgue-class measure, called the Masur-Veech measure. Masur-Veech volumes are intimately connected to counting square-tiled surfaces in a given stratum. It is also interesting to study general affine measures (supported on affine invariant submanifolds). By work of Eskin-Mirzakhani-Mohammadi, many dynamical questions can be reduced to the study of these affine measures. It is natural to ask about the interaction between measures of certain subsets of surfaces and the geometric properties of those surfaces. I will discuss a proof in progress of a conjecture on the volume, with respect to any affine measure, of the locus of surfaces that have multiple independent short saddle connections. A key tool is the new compactification of strata due to Bainbridge-Chen-Gendron-Grushevsky-Moller, which gives a good picture of how a translation surface can degenerate. The techniques also give a new proof of the following very recent result of Duc-Manh Nguyen (possibly of interest to reptilers): the natural measure on a stratum of higher order differentials is finite.
• Saturday 6:30-? DownTown Conference Dinner
  The Place abstract± The place we're eating is called "The Place."
• Sunday 9-? CoverdellS175 Pastries & Coffee
  TBA abstract± TBA
• Sunday 10-? CoverdellS175 Vanya Telpukhovskiy
  On normalizations of Thurston measure on the space of measured laminations abstract± The space of measured laminations ML(Sigma) associated to a topological surface Sigma of genus g with n punctures is an integral piecewise linear manifold of real dimension 6g-6+2n. There is also a natural symplectic structure on ML(Sigma) defined by Thurston. The integral and symplectic structures define a pair of measures on ML(Sigma) which are known to be proportional. The projective class of these measures on ML(Sigma) is called the Thurston measure. I will compute the ratio between two normalizations of the Thurston measure and talk about its relation to counting problems for quadratic differentials, in particular square-tiled surfaces (if time allows). This work is joint with Leonid Monin.
• Sunday 11:30-? CoverdellS175 David Gay
  Tiling questions motivated by the search for interesting trisection diagrams abstract± TBA
• Sunday 1:30-? CoverdellS175 Math Discussion Time
  A Time to Discuss Math abstract± When the math will be discussed.