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Algebraic Geometry

2025 Georgia Algebraic Geometry Symposium Website

Permanent faculty and their fields of interests

Valery AlexeevProfessor, Ph.D. Moscow University 1990. Degenerations and compact moduli spaces of algebraic varieties, including curves, surfaces, abelian varieties, other varieties with group action. Birational geometry and Minimal Model Program. Singularities appearing in MMP. Toric and spherical varieites. Derived categories. Extremal metrics.

Hülya Argüz, Assistant Professor, Ph.D. University of Hamburg, 2016. Enumerative algebraic geometry: Gromov-Witten theory and DT theory of quiver representations. Logarithmic and tropical geometry. Mirror symmetry. Cluster varieties.

Pierrick Bousseau, Assistant Professor, Ph.D. Imperial College London, 2018. Curve counting theories, including Gromov-Witten and Donaldson-Thomas invariants. Tropical geometry and mirror symmetry. Deformation quantization and mathematical physics.

Jimmy Dillies, Lecturer, Ph.D. University of Pennsylvania, 2006. Automorphisms of K3 surfaces and construction of Calabi-Yau varieties.

William GrahamProfessor, Ph.D. Massachusetts Institute of Technology 1992. Geometry related to algebraic groups: equivariant K-theory, cohomology, and Chow groups; flag varieties, Schubert calculus, and related combinatorics.

Dino LorenziniProfessor, Ph.D. U.C. Berkeley, 1988. Rational points on algebraic varieties. Torsion points on abelian varieties. Néron models of abelian varieties. Modular curves and their jacobians. Models of curves and wild ramification. Wild quotient singularities of surfaces.

Adjunct and Emeritus Faculty

Philip Engel, Adjunct Assistant Professor, Ph.D. Columbia 2015.  Complex surface singularities. Moduli of K3 surfaces and anticanonical pairs. Mirror symmetry, tropicalization, and integral-affine structures. Flat structures on Riemann surfaces. Enumeration of tilings and Hurwitz theory. Penrose tilings.

Mitchell RothsteinProfessor Emeritus, Ph.D. UCLA, 1984. Retired in 2021. Algebro-geometric methods in Mathematical Physics. Fourier-Mukai transforms, D-modules and integrable systems. Supervarieties.

Roy SmithProfessor Emeritus, Ph.D. University of Utah, 1977. Retired in 2010. Geometry of polarized abelian varieties and their moduli spaces, especially Jacobian and Prym varieties, Torelli problems, deformations of singularities.

Robert VarleyProfessor Emeritus, Ph.D. University of North Carolina, 1977. Retired in 2016. Algebraic geometry, curves, abelian varieties, theta divisors, deformation theory, algebraic topology of varieties, mathematical aspects of quantum field theory.

Postdoctoral Associates and their fields of interest

Soumya Sinha Babu, Limited Term Assistant Professor, Ph.D. Washington Univ. in St. Louis, 2022.  Hodge Theory (computing regulators and constructing higher normal functions on higher algebraic cycles), and high energy physics (using Mirror Symmetry to investigate limiting behavior of generalized periods and spectrum of quantum operators).

Minyoung Jeon, Postdoctoral Research and Teaching Associate, Ph.D. The Ohio State University, 2022. (Combinatorial) algebraic geometry. Schubert varieties and degeneracy loci. Intersection and cohomology theory, Grassmannians and flag varieties. Application of Schubert Calculus to various topics, which include but not limited to the geometry of algebraic curves and their moduli.

Alberto San Miguel Malaney, Limited Term Assistant Professor, Ph.D. University of Texas, 2024. Geometric representation theory: symplectic singularities and their partial resolutions, Springer theory, perverse sheaves. Birational geometry and deformation theory.

37 graduates and their dissertations


Haiyang Wang  (Dino Lorenzini), Three topics in Number Theory.


Nolan Schock (Valery Alexeev), Geometry of Tropical Compactifications of Moduli Spaces.

Arvind Suresh (Dino Lorenzini), Realizing Galois Representations in Abelian Varieties by Specialization.


Mentzelos Melistas (Dino Lorenzini), Reduction and Torsion Points of Abelian Varieties.

Makoto Suwama (Dino Lorenzini), Two Topics in Algebra and Number Theory.


Xian Wu (Valery Alexeev/Noah Giansiracusa), Stable pair compactification of the moduli space of two special families of calabi-yau 3-folds and chow quotients of grassmannians by diagonal subtori


Brian Bonsignore (Robert Varley), Cohomological n-equivalence in differential graded algebras.

Natalie L. Hobson (Angela Gibney), Vector bundles of conformal blocks in types A and C from a combinatorial approach.

Luca Schaffler (Valery Alexeev), The KSBA compactification of a 4-dimensional family of polarized Enriques surfaces.


Patrick K. McFaddin (Daniel Krashen), K-cohomology of generalized Severi-Brauer varieties.

Matthew Zawodniak (Robert Varley), A moduli space for rational homotopy types with the same homotopy Lie algebra.


Adrian Brunyate (Valery Alexeev), A modular compactification of the space of elliptic K3 surfaces. NSF postdoctoral fellowship (2015-2018).


Xiaoyan (Shannon) Hu (Valery Alexeev), The compactifications of moduli spaces of Burniat surfaces with 1 < K2 < 6.

Joseph Tenini (Valery Alexeev), Results on an extended Torelli map and singularities of degenerate abelian varieties.


Jae Ho Shin (Valery Alexeev), The reduction map for the moduli spaces of weighted hyperplane arrangements.

David Krumm (Dino Lorenzini), Quadratic points on modular curves.

Maurice J. LeBlanc, III, (Robert Varley), Analyzing free quantum fields theories on the ax+b space-time and Wigner contractions to the Minkowski plane.


Wenjing Li (William Graham), Spiral Schubert varieties in type extended A2.

Brandon Samples (William Graham), Components and Springer fibers for the exceptional groups G2 and F4.

Ben Wyser (William Graham), Symmetric subgroup orbit closures on flag varieties: their equivariant geometry, combinatorics, and connections with degeneracy loci. UGA Presidential Fellowship 2006-11. NSF International Research Fellowship, Institut Fourier, Grenoble, France, 2013-2015.

Jim Stankewicz (Dino Lorenzini and Pete Clark), Twists of Shimura curves.


Maxim Arap (Elham Izadi), Tautological rings of Prym varieties.

Justin Manning (Robert Varley), Axiomatic quantum fields on the de Sitter surface.


Jeremiah Hower (Dino Lorenzini), On elliptic curves and arithmetical graphs.


Michael Guy (Valery Alexeev), Moduli of weighted stable maps and their gravitational descendants.

Valerie Hower (Clinton McCrory), Hodge Spaces of Real Toric Varieties.

Peter Petrov (Valery Alexeev), Nash problem on spaces of arcs.

Joe Rusinko (Valery Alexeev), Equivalence of mirror families constructed from toric degenerations of flag varieties.


Sungkon Chang (Dino Lorenzini), The arithmetic of twists of superelliptic curves.


Tawanda Gwena (Valery Alexeev), Degenerations of Prym varieties and cubic threefolds.

Rene-Michel Shumbusho (Dino Lorenzini), Elliptic curves with prime conductor and a conjecture of Cremona.


Vitaly Vologodsky (Valery Alexeev), The extended Torelli and Prym maps.

Daniele Arcara (Elham Izadi) Moduli spaces of vector bundles on curves.


Dennis Wayne Tarrant (Robert Varley) Term orders on the polynomial ring and the Grobner fan of an ideal.

Janice Wethington (Robert Varley) On computing the Thom-Boardman symbols for polynomial multiplication maps.


Huasong Yin  (Robert Varley) Deformation of Special Subvarieties of Divisors Associated to Double Covers of Genus Three Curves.


Shoji Yokura (Clinton McCrory) Polar Classes and Segre Classes on Singular Projective Varieties.