Research Interests

Anar Akhmedov's research interests span diverse mathematical disciplines, including low-dimensional topology, symplectic/contact topology, gauge theory, algebraic geometry, group theory, and topological data science. His work has predominantly focused on low-dimensional topology, with contributions to areas such as the classification of smooth and symplectic 4-manifolds, exotic smooth structures on 4-manifolds, and Stein fillings of contact 3-manifolds. Akhmedov also explores elliptic curves and higher-dimensional varieties, emphasizing the study of rational points. Recently, he has also developed a strong interest in topological data science, investigating its potential applications in data analysis.

Research Website

Education

• BA: Mathematics, California State University, Fresno, 2000
• PhD: Mathematics, University of California at Irvine, 2006

Scientific & Professional Societies

Currently Teaching Courses

• Fall 2023 – MATH 1571H: Honors Calculus I
• Fall 2023 – MATH 8360: Topics in Topology
• Spring 2024 – MATH 8360: Topics in Topology

Honors and Awards

1. American Mathematical Society Fellow for 2020 (for contribution to core problems in topology).
2. Humboldt Research Fellowship for Experienced Researchers, Germany, 2020-2023.
3. Simons Research Fellowship, 2018-19.
4. Alfred P. Sloan Research Fellowship, 2012-16.
5. University of Minnesota Guillermo E. Borja Award (in recognition of research and scholarly accomplishments), 2013.
6. William Hodge Fellowship, IHES, 2008 (declined). 
7. International Mathematical Olympiad: bronze medal, 1993  
8. Azerbaijan National Mathematical Olympiad: 1st place 1993. 
9. “Quantum” Mathematical Contest of Russian Academy of Science for high school students in former USSR: winner 1992-94  

Selected Publications

1. Akhmedov, Anar and Park, B. Doug "Exotic smooth structures on small 4-manifolds". Invent. Math. 173 (2008), no. 1, 209–223
2. Akhmedov, Anar and Park, B. Doug "Exotic smooth structures on small 4-manifolds with odd signatures". Invent. Math. 181 (2010), no. 3, 577–603
3. Akhmedov, Anar "Small exotic 4-manifolds". Algebraic and Geometric Topology. 8 (2008), no. 3, 1781–1794.
4. Anar Akhmedov, “Symplectic Calabi-Yau 6-Manifolds”, Advances in Mathematics, 261 (2014), 115-125.
5. Anar Akhmedov, Masashi Ishida, and B. Doug Park, “Reducible Smooth Structures on 4-Manifolds with Zero Signature”, Journal of Topology, 7(3) (2014), 607-616
6. Anar Akhmedov and Ludmil Katzarkov, “Symplectic Surgeries Along Certain Singularities and New Lefschetz Fibrations”, Advances in Mathematics, 360 (2020).
7. A. Akhmedov, C. Karakurt, and Sumeyra Sakallı, Generalized Chain Surgeries and Applications, Journal of Symplectic Geometry, Vol. 19, No. 5 (2021), pp. 1047-1069.
8. Anar Akhmedov, Sumeyra Sakallı, and B. Doug Park, “Exotic Smooth Structures on Connected Sums of S^2 x S^2”, The Quarterly Journal of Mathematics, Volume 74, Issue 2, June 2023, Pages 799–809.