RTG fellowships for graduate students are intended to allow graduate students significant time for research, course work, and related activities. Each year, the RTG grant will support, on average, 2 pre-candidacy students (one semester each) and 3 post-candidacy students (full year each).

Information on the graduate program at The Ohio State University (and for more information) can be found here. To apply to the program, , follow the instructions on the official website, available at this link. You must apply to be admitted as PhD student in Mathematics. If you are interested in being part of the RTG group, please mention it in your application form. Deadline for 2024 has already passed. The new round of applications will be open in Autumn 2024.

Past and current RTG graduate student fellows can be found here.

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Thematic years, RTG Workshop and Retreat

The graduate and postdoctoral training supported by the RTG award is anchored on five thematic years emphasizing different aspects of our combinatorial, arithmetic, and topological approaches to study algebraic varieties. Focused topics courses and research training seminars running each year will be complemented by an RTG Workshop hosting external PhD students for mini-courses by two outside experts, followed by a Group Retreat featuring a period of intensive mathematical collaboration, and promoting community-building through a goal-oriented activity. More information can be found here.

In preparation to the these activities, faculty in our group will run graduate topics courses related to the subjects central to the following year's mathematical theme. For more information on these activities, follow this link.

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• MATH 8500 - Topics in Combinatorics: Approximate Groups. Instructor: Yifan Jing.


• MATH 8120 - Topics in Number Theory. Instructor: Stefan Patrikis.


• MATH 7141 - Basic Algebraic Geometry I. Instructor: David Anderson

• MATH 8120 - Topics in Number Theory: The arithmetic of elliptic curves. Instructor: Tyler Genao.


• MATH 7142 - Basic Algebraic Geometry II. Instructor: Stefan Patrikis.


• MATH 7122 - Analytic Number Theory. Instructor: Jennifer Park


• MATH 6131 - Introduction to Representation Theory. Instructor: Sachin Gautam.

• MATH 8140 - Introduction to Combinatorial Algebraic Geometry. Instructor: David Anderson


• MATH 7141 - Basic Algebraic Geometry I. Instructor: Eric Katz


• MATH 7121 - Algebraic Number Theory. Instructor: Wenzhi Luo

• MATH 8120 - Topics in Number Theory. Instructor: Jennifer Park.


• MATH 7142 - Basic Algebraic Geometry II. Instructor: Stefan Patrikis.


• MATH 6131 - Introduction to Representation Theory. Instructor: Sachin Gautam.

• MATH 7141 - Basic Algebraic Geometry I. Instructor: Maria Angelica Cueto

• MATH 8140 - Topics in Algebraic Geometry: Riemann Surfaces. Instructor: Maria Angelica Cueto

• MATH 8120 - Topics in Number Theory: Étale Cohomology. Instructor: Stefan Patrikis.

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Learning Seminars

The affine Grassmannian, quantum cohomology and the Peterson/Kato Theorems

• 
  The long-term goal is to understand the following three foundational papers:
  
  
  1. Peterson, unpublished handwritten notes from his 1997 MIT lectures.
  2. Thomas Lam and Mark Shimozono: "Quantum cohomology of G/P and homology of affine Grassmannian",
  3. Syu Kato: Loop structure on equivariant K-theory of semi-infinite flag manifolds".
  
  The basic geometric and combinatorial structure of the affine Grassmannian and related spaces.

Preliminary meeting: Friday August 29, 2:00-3:00pm in Math Tower MW 154.


• Meetings: TBD

Weyl conjectures, perverse sheaves, Hodge Theory, l-adic cohomology and beyond Seminar

• A detailed syllabus can be found here.
  


• Meetings: Thursdays 3:00-4:30pm, Enarson Classroom Building EC 354.

Weil II and Perverse Sheaves Seminar

• Syllabus: This seminar will study the theory of weights for l-adic sheaves on varieties over finite fields, particularly the generalization of the Riemann hypothesis to the relative setting as first developed in:
  
  Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. (1980), no. 52, 137-252. MR 601520 (83c:14017).
  
  With the remaining time, we will introduce perverse sheaves in the arithmetic setting.
  A detailed syllabus can be found here.


• Prerequisites: a first course in scheme theory (as in the 714x sequence) is essential, and experience with étale cohomology (as in last fall's topics course) is ideal. The preliminary meeting will review some of the important background and assign speakers to future talks.
  


• Preliminary meeting: Friday August 25, 3:00-4:30pm in Cockins Hall CH 228.


• Meetings: Fridays 3:30-5:00pm, Bakers Systems Engineering BE 136.

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Research Seminars

• Algebraic Geometry Seminar


• Arithmetic Geometry Seminar


• Number Theory Seminar


• Representation Theory Seminar

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Back to the main website of the RTG: "Arithmetic, Combinatorics, and Topology of Algebraic Varieties".

The Ohio State University, Department of Mathematics, 231 W. 18th Avenue, Columbus, OH, 43210, USA.