# posters

**Poster Session**

12-1:15 pm, Bell Art Gallery

**Tropical complexes **Dustin Cartwright (Yale)

Tropical complexes are generalizations of tropical curves to higher dimensions. I will present some comparison theorems between tropical curves and algebraic varieties.

**Sharp slope bounds for sweeping families of trigonal curves **Anand Deopurkar (Columbia) and Anand Patel (Harvard)

We establish sharp bounds for the slopes of curves in Mg that sweep the locus of trigonal curves, proving Stankova-Frenkel’s conjectured bound of 7+6/g for even g and obtaining

the bound 7+20/(3g+1) for odd g.

**Regular Nilpotent Hessenberg Varieties: Fixed Points and Equivariant Cohomology **Elizabeth Drellich (UMass Amherst)

**On the Harbourne-Hirschowitz Conjecture in $P^{n}$** Olivia Dumitrescu (UC Davis)

**A nonabelian Hodge theorem for twisted vector bundles** Alberto Garcia-Raboso (UPenn)

We prove an extension of the nonabelian Hodge theorem in which the underlying objects are twisted vector bundles over a smooth complex projective variety.

**Operational Algebraic Cobordism** Jose Gonzalez (UBC)

We associate a bivariant theory to any given oriented Borel-Moore pre-homology theory in the category of algebraic schemes, and more generally to any given oriented Borel-Moore pre-homology theory in a suitable category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational G-equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational T-equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring. These results are from joint work with Kalle Karu.

**Brill-Noether Theory of Tropical Curves** Yoav Len (Yale)

**An R-Divisor with Non-closed Restricted Base Locus** John Lesieutre (MIT)

We exhibit a pseudoeffective $\R$-divisor $D$ on the blow-up of $\P^3$ at nine very general points which lies in the closed movable cone and has negative intersections with a Zariski dense set of curves. It follows that the restricted base locus $\Bm(D) =\bigcup_{\text{$A$ ample}} \B(D+A)$ is not closed and that $D$ does not admit a Zariski decomposition in even a very weak sense.

**Regular del Pezzo Surfaces with Irregularity**** **Zachary Maddock (Columbia)

Two examples are constructed of del Pezzo surfaces X that are regular but not smooth over an imperfect field and have irregularity h^1(X,\OO_X) = 1. A linear inequality is given between the integers q and d that can arise as irregularity q = h^1(X,\OO_X) and degree d = K_X^2 of a normal l.c.i. del Pezzo surface X with irregularity (i.e. h^1(X,\OO_X) \neq 0).

**Some examples of tilt-stable objects on threefolds** Yogesh More (SUNY Old Westbury)

We study the notion of tilt-stability introduced by Bayer, Macri, and Toda in their conjectural construction of a Bridgeland stability condition on any smooth complex threefold. This is joint work with Jason Lo.

**On (2,4) Calabi-Yau Complete Intersections that contain an Enriques Surface** Howard Nuer (Rutgers)

We study nodal complete intersection threefolds of type $(2,4)$ in $\PP^5$ which contain an Enriques surface in its Fano embedding. We completely determine Calabi-Yau birational models of a generic such threefold. These models have Hodge numbers $(h^{11},h^{12})=(2,32)$. We also describe Calabi-Yau varieties with Hodge numbers equal to $(2,26)$, $(23,5)$ and $(31,1)$. The last two pairs of Hodge numbers are, to the best of our knowledge, new.

**The geometry of the moduli space of minimal dominant rational curves on algebraic variety** Xuanyu Pan (Columbia)

**Abelian fibrations associated to linear systems on Enriques surfaces** Giulia Saccà (Princeton)

**Vojta-Lang Conjecture over function ﬁelds: from Arithmetic to Geometry** Amos Turchet (Università degli studi di Udine)

We will present some recent results for Vojta-Lang conjecture over function ﬁelds for complements of a normal crossing divisor D in P2(C) focusing on a worked extension of the results of Corvaja and Zannier in the case where D is a union of a conic and two lines in general position [paper in preparation by the author]. We will address some ways of generalize this to two-component divisors.

**Representation and Hilbert Schemes of Points on K3 Surfaces** Letao Zhang (Rice)

Let X denote a general deformation of the Hilbert schemes of n points on K3 surfaces, and Gx be the associated group acting on the cohomology ring. We computed the graded character formula associated to the Gx actioin on the cohomology ring of X. Also, we could use the formula to deduct the generating series of the number of canonical Hodge classes for each n.