Donu's 60th Birthday Conference
September 12th  15th, 2019
Speakers
 Christine Berkesch (University of Minnesota)
On the parametric variation of the solution spaces of an Ahypergeometric system.
We survey the variation with respect to parameters of the solution space of an Ahypergeometric system, including joint
works with Barrera, Fern´andezFern´andez, Forsg˚ard, and Matusevich.
 Roya Beheshti
Moduli spaces of rational curves on Fano hypersurfaces.
I will talk about the geometry of moduli spaces of rational
curves and linear subvarieties on smooth Fano hypersurfaces and
discuss the dimension and irreducibility of these moduli spaces.
I will also talk about some nonpositivity results for spaces of rational
curves on Fano hypersurfaces of low index.
 Lawrence Ein (UIC)
Singularities and syzgies of secant varieties of nonsingular projective curves
Let C be a smooth projective curve of genus g and C is embedded into the projective space by a very ample complete linear
system L. For each positive integer k, we consider the kth secant varieity \( Sec_k (C,L) \),
We show that if \( \deg L \ge 2g+1+2k\). Then \( Sec_k(C,L) \) is projectively Cohen Macaulary.
Furthermore, \( Sec_k(C, L)\) has normal Du Bois singularities. This is joint work with Wenbo Niu and Jinhyung Park.
 Edray Goins (Pomona College)
Metabelian Galois Representations
We are used to working with Galois representations associated to elliptic curves by considering the action of the absolute
Galois group on torsion points. However there is a slightly more exotic way to view this construction once we realize that
the Tate module of an elliptic curve is just the abelianization of the ´etale fundamental group of the punctured torus.
In this talk, we discuss how to construct a class of Galois representations by considering covers of elliptic curves which
are branched over one point. We discuss how this is related to the question of surjectivity of certain Galois representation,
and how to construct representations with image isomorphic to the holomorph of the quaternions. We will not assume
extensive knowledge of ´etale cohomology. This is joint work with Rachel Davis
 Feng Hao (LMU München)
Projective threefolds admitting nowhere vanishing holomorphic 1forms.
A celebrated result of Popa and Schnell states that on a smooth complex projective variety of general type any holomorphic
1form has at least one zero, so the existence of a holomorphic 1form without zeros forces the variety to be of special type.
In this talk I will give a full classification of smooth projective threefolds which admit nowhere vanishing holomorphic
1forms. This is a joint work with S. Schreieder.
 Elham Izadi (UCSD)
Surfaces generating the space of Hodge classes in the cohomology of theta divisors of dimension 4.
For the theta divisor of a generic principally polarized abelian variety of dimension 5,
the space of degree 4 Hodge classes is of dimension 7. We produce 27 surfaces, obtained as
special subvarieties for Prym structures on the abelian variety, which generate this 7dimensional
space over the rational numbers. We show that the sublattice generated by the cohomology classes of these
surfaces is (up to a multiple of 2) isomorphic to the Picard lattice of a generic cubic surface.
This is joint work with Jonathan Conder and Edward Dewey.
 Matt Kerr (Washington University in St. Louis)
Hodge theory of degenerations.
The asymptotics and monodromy of periods in degenerating families of algebraic varieties are encountered in many
settings — for example, in comparing various compactifications of moduli, in computing limits of invariants of algebraic
cycles, and in topological string theory. In this talk, based on joint work with Radu Laza and Morihiko Saito, we shall
describe several tools (building on classical work of Milnor, Deligne, and Clemens) for comparing the Hodge theory of
singular fibers to that of their nearby fibers, and touch on some relations to birational geometry.
 Laurentiu Maxim (University of WisconsinMadison)
Measuring the complexity of hypersurface singularities in algebraic geometry and topology
I will discuss two different ways to measure the complexity of singularities of a (globallydefined)
complex hypersurface. The first is derived via (Hodgetheoretic) characteristic classes of singular
complex algebraic varieties, while the second is provided by the multiplier ideals. I will also point
out a natural connection between these two points of view. (Joint work with Morihiko Saito and
Joerg Schuermann.)
 Mircea Mustata (University of Michigan)
Hodge filtration, minimal exponent, and local vanishing
I will discuss a circle of ideas relating Saito’s minimal exponent of a singularity, the Hodge filtration on the localization
along a regular function, the Vfiltration of Malgrange and Kashiwara, and local vanishing for differential forms with log
poles. This is based on joint work with Mihnea Popa
 Madhav Nori (University of Chicago)
Hypergeometric Motives
IThis is a report on ongoing joint work with Deepam Patel. We will discuss
some analogues of Grothendieck's comparison theorems that have been obtained in this context,
and an application to local monodromy.
 Jinhyun Park (KAIST)
On extension of the motivic cohomology to singular kschemes
In this talk, I will take about a recent new approach on the question of extending the motivic cohomology theory on
smooth kschemes to singular ones. I will first briefly explain what motivic cohomology is (or should be), and sketch
the idea of the new construction.
I will discuss some results obtained in the process, and some potential applications as well. If time permits, some works in progress will be mentioned, too. Some of them are jointly studied with Sinan Ünver.
 Mihnea Popa (Northwestern University)
Minimal exponents of singularities
The minimal exponent of a function is the negative of the largest root of its reduced BernsteinSato polynomial.
It refines the notion of log canonical threshold, and it is related (sometimes conjecturally) to other
interesting invariants. I will describe some results towards understanding minimal exponents, based on viewing
them in the context of Dmodules and Hodge theory on one hand, and birational geometry on the other.
This is joint work with Mircea Mustata, whose lecture will present further joint results regarding minimal exponents.
 Alex Suciu (Northweastern University)
Cohomology jump loci in geometry and topology
Twentysomeodd years ago, Donu Arapura wrote the paper
``Geometry of cohomology support loci for local systems."
To this day, this seminal paper provides inspiration
and guides the work of geometers and topologists
alike. I will discuss some recent developments in the
theory, especially in regards to duality and finiteness
properties of spaces and groups, and I will outline
some applications to complex algebraic geometry
and lowdimensional topology.
 Uli Walther(Purdue University)
Weight filtration on Hodge modules coming from toric embeddings.
We describe the weight filtration on the Hodge module that arises as direct image of the structure sheaf of the dtorus
under the toric (monomial) map induced by the d by n integer matrix A, if the semigroup of A is saturated. The graded
parts are combinatorial ad not arithmetic, and express the failure of the cone of A to be simplicial.
 Jaroslaw Wlodarczyk (Purdue University)
Desingularization of schemes and morphisms.
We review some recent results on desingularization of schemes, and morphisms. In a joint paper by Abramovich Temkin
Wlodarczyk we give a proof of canonical resolution of singularities of the varieties in charactersitic zero, which is functorial
with respect to logarithmically smooth morphisms. The results and the method are extended in the subsequent paper
to the canonical desingularization of morphisms. The method requires use of more general centers with monomials in
the logarithmic structure allowing fractional exponents. This can be further extended in a recent paper on the canonical
desingularization which uses weighted blowups. Such algorithm uses natural weights associated with a sequence of
maximal contacts and leads to the direct improvement of the resolution invariant.
On the other hand when combined functorial toroidal desingularization with the author’s recent result on the canonical
desingularization of locally binomial varieties, one proves a canonical desingularization of varieties except of toroidal locus.
It modifies a variety without affecting toroidal singularities. The resulting singularities are exactly the same as the ones in
the untouched toroidal locus. The result gives, in particular, a toroidal compactification of toroidal varieties.
 SaiKee Yeung (Purdue University)
Torelli locus and locally symmetric subspaces of a Siegel modular variety
The purpose of the talk is to explain some geometric approaches to study whether it
is possible to realize a locally symmetric space as a totally geodesic subvariety in the
Torelli locus of a Siegel modular variety. Restricting to locally Hermitian symmetric
subvarieties of a Siegel modular variety, the problem is related to conjectures of Coleman and Oort.
Logistics
Department of Mathematics, Madison Wisconsin.
September 1213th 2019 : Van Vleck Hall 911
September 1415th 2019 : Van Vise Hall 399
Here is some general information about getting to the mathematics department at the University of Wisconsin, Madison.
Schedule
Thursday 12th. Sept 
Friday 13th Sept. 
Saturday 14th Sept. 
Sunday 15th. Sept. 




8.309.20 
Roya Beheshti 


9:3010:20 
Elham Izadi 
9:3010:20 
Larentiu Maxim 
9.3010.20 
Feng Hao 
99.50 
Christine Berkesch 
1111.50 
Alex Suciu 
1111.50 
SaiKee Yeung 
10.3011.20 
Matt Kerr 
1010.50 
Edray Goins 
1.302.20 
Madhav Nori 
1.302.20 
Jinhyun Park 
2.002.50 
Jaroslaw Wlodarczyk 


2.303.20 
Mihnea Popa 
2.303.20 

33.50 
Mircea Mustata 






4.004.50 
Uli Walther 


On Saturday evening there will be a banquet at restaurant Ichiban.