The following is a tentative program schedule for the Texas Geometry and Topology Conference. Please check back here for the most up-to-date information.

Friday Schedule – Math Building Room 11

Time Speaker Title Abstract
3:00 pm – 4:00 pm Banquet – Math Building Main Floor and Room 106 Tutoring Center
4:00 pm – 4:50 pm Catherine Searle When is an Alexandrov space smoothable? Alexandrov spaces of finite dimension n≥1 are locally compact, locally complete, length spaces with a lower curvature bound in the triangle comparison sense. They are a natural generalization of Riemannian manifolds with a lower sectional curvature bound. In this talk, I will discuss the problem of when an Alexandrov space is smoothable. We will review the history of this question and discuss a new result that partially answers it. This is joint work with Pedro Solórzano and Fred Wilhelm.

Saturday Schedule – Math Building Room 11

Time Speaker Title Abstract
9:00 am – 9:30 am Registration and Breakfast/Coffee
9:30 am – 10:20 am Brian Lawrence Rational points and computational complex analysis A classic problem in number theory asks to find all rational solutions to a polynomial equation f(x,y)=0 – geometrically, all rational points on an algebraic curve. I will briefly survey some attacks on this problem: Chabauty's method, quadratic Chabauty, and "Chabauty on covers". Motivated by this problem, I will suggest one or two problems in computational complex analysis.
10:30 am – 11:20 am Rui Loja Fernandes Invariant Kähler metrics for toric fibrations In this talk, I will discuss (extremal) invariant Kähler metrics for Lagrangian fibrations admitting only elliptic singularities. It turns out that such fibrations are precisely the Hamiltonian spaces of toric actions of symplectic torus bundles, which are a special type of symplectic groupoid. This allows us to extend the Abreu-Guillemin-Donaldson theory of invariant (extremal) Kähler metrics from toric manifolds to a much larger class of symplectic manifolds. This presentation is based on ongoing joint work with Miguel Abreu (IST-Lisbon) and Maarten Mol (Max Planck-Bonn).
11:30 am – 12:20 pm Yi Lai Riemannian and Kähler flying wing steady Ricci solitons Steady Ricci solitons are fundamental objects in the study of Ricci flow. We constructed a family of flying wing steady solitons in any real dimension n≥3, confirming a conjecture by Hamilton. In dimension 3, all steady gradient solitons are O(2)-symmetric. In the Kähler case, we also construct a family of Kähler flying wing steady gradient solitons with positive curvature for any complex dimension n≥2. This is partly collaborated with Pak-Yeung Chan and Ronan Conlon.
12:30 pm – 2:00 pm Lunch Break and Informal Discussions
2:00 pm – 2:50 pm Franz Pedit Higgs bundles, affine spheres, Monge-Ampere equations, and SYZ mirror symmetry In this talk I shall explain how to construct special Lagrangian 3-torus fibrations, singular over a trivalent discriminant locus, of Calabi-Yau 3-folds using parabolic non-Abelian Hodge theory. The results are joint work with Sebastian Heller (BIMSA, Beijing) and Charles Ouyang (Washington University, St. Louis).
3:00 pm – 3:50 pm Thomas A. Ivey mKdV Flows for Legendrian Curves in the 3-sphere As the unit sphere in C², the 3-sphere is acted on by U(2), preserving the standard contact structure generated by planes orthogonal to the Hopf fibers. We define a natural symplectic structure on the space of periodic Legendrian curves and identify an infinite hierarchy of commuting Hamiltonian flows which induce the modified Korteweg-DeVries hierarchy. This is joint work with Annalisa Calini and Emilio Musso.
4:00 pm – 4:50 pm Joel Langer Quadratic Differentials and Plane Curves The notion of quadratic differential Q=q(z)dz² was developed in the twentieth century as a tool in Riemann surface theory. This talk explores how the concept also provides an ideal language for revisiting topics in the classical theory of real algebraic plane curves, including the clinant and focal quadratic differentials, Kiepert sextic, Story's hyperbolic conics, Siebeck's bicircular quartics, and the Edwards theory of elliptic curves.
5:30 pm – 8:00 pm Dinner and Discussions – Triple J Chophouse (limited reservations; rides must be requested in advance)

Sunday Schedule – Math Building Room 11

Time Speaker Title Abstract
10:00 am – 11:00 am Igor Zelenko On projective and affine equivalence of sub-Riemannian metrics: generalized Eisenhart and Levi-Civita theorems Sub-Riemannian metrics on a manifold are defined by a distribution together with a Euclidean structure on each fiber. Two metrics are projectively equivalent if they share geodesics up to reparameterization, and affinely equivalent if they share geodesics up to affine reparameterization. We describe recent progress toward the generalization of the classical results of Levi-Civita (1898) and Eisenhart (1923) to sub-Riemannian metrics. The talk is based on joint works with Frederic Jean, Sofya Maslovskaya, Zaifeng Lin, and Christopher Sinkule.
11:00 am – 12:00 pm Conclusion

Program Schedule – Location

The conference will be held in the Mathematics and Statistics Building, Room 11, at Texas Tech University, Lubbock, TX.