Anar Akhmedov's Homepage
Anar Akhmedov

School of Mathematics
University of Minnesota
Office:  Vincent Hall, Room 355,
Office Phone: 612-624-5224
I am a Professor in the School of Mathematics at University of Minnesota. Before joining the University of Minnesota, I was a Visiting Assistant Professor at Georgia Tech and University of Zurich from 2006 - 2008, then a Ritt Assistant Professor at Columbia University from 2008-2009. I have also held Visiting Professor positions at University of Vienna, Austria and at Harvard University as Simons Fellow . My research interests are low-dimensional topology, smooth 4-manifolds, and symplectic topology. I am also interested in algebraic geometry.

I gratefully acknowledge the supports received from the Alfred P. Sloan Foundation, The National Science Foundation (NSF DMS: 1005741, NSF FRG DMS-1065955), Simons Foundation and Alexander von Humboldt Foundation.
Seminars: Differential Geometry and Symplectic Topology, Topology, and other math seminars at University of Minnesota

Workshop on Topology and Invariants of 4-Manifolds
August 23 to August 27, 2014
Simons Center for Geometry and Physics
Workshop and Conference on the Topology and Invariants of Smooth 4-Manifolds
July 31 to August 10, 2013
University of Minnesota
Workshop and Conference on Holomorphic Curves and Low Dimensional Topology
July 30 to August 11, 2012
Stanford University
Fifth Yamabe Symposium

Ph.D. Students

Publications and Preprints

  1. Symplectic surgeries along certain singularities and new Lefschetz fibrations, with L. Katzarkov, Advances in Mathematics, 360 (2020).
  2. The existence of an indecomposable minimal genus two Lefschetz fibration, with Naoyuki Monden, in press, Osaka Journal of Mathematics (2020).
  3. Exotic smooth structures on connected sums of S^2 x S^2, with B. D. Park, and S. Sakalli (2019), submitted
  4. Geography of simply connected nonspin symplectic 4-manifolds with positive signature II, with B. D. Park (2019), submitted
  5. Lefschetz fibrations via monodromy substitution, with N. Monden and S. Sakalli, preprint.
  6. Genus two Lefschetz fibrations with b_{+}=1 and c_1^2=1,2, with Naoyuki Monden, in press, (2019).
  7. Geography of simply connected spin symplectic 4-manifolds, II with D. Park, Comptes Rendus Mathematique, 357(3), 296-298. (2019).
  8. Deformation of singular fibers of genus two fibrations and small exotic symplectic 4 -manifolds, with S. Sakalli, International Journal of Mathematics, Vol. 30, No. 03, 2019.
  9. New Symplectic 6-Manifolds via Coisotropic Luttinger Surgery, Advanced Mathematical Models & Applications. 2018, Vol.3, No.2, 2018, 106-116.
  10. Exotic Stein fillings with arbitrary fundamental group, with B. Ozbagci, Geometry Dedicata, (2017).
  11. Constructing Lefschetz fibrations via daisy substitutions, with Naoyuki Monden, Kyoto Journal of Mathematics Math. 56 Number 3 (2016), 501-529.
  12. On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature , with Sakalli, S., Topology and its Applications (2016), 206, 24-45.
  13. Dissolving 4-manifolds, covering spaces and Yamabe invariant, with M. Ishida, and D. Park, Ann Glob Anal Geom, 47 (2015), 271-83.
  14. New exotic 4-manifolds via Luttinger surgery on Lefschetz fibrations, with Saglam, K. N., International Journal of Mathematics (2015), 26, No. 1.
  15. Reducible smooth structures on 4-manifolds with zero signature, with M. Ishida, and D. Park, Journal of Topology, 7 (2014), no. 3, 607-616.
  16. Symplectic Calabi-Yau 6-Manifolds, Advances in Mathematics, 262 (2014), 115-125.
  17. Singularity links with exotic stein fillings, with Ozbagci, B., Journal of Singularities (2014), no. 8, 39-49.
  18. Lantern substitution and new symplectic 4-manifolds with b_2+ = 3, with Park, J. Y., Mathematical Research Letters (2014), 21, no. 1, 1-17.
  19. Geography of simply connected nonspin symplectic 4-manifolds with positive signature, with Hughes, M. C. & Park, B. D., Pacific Journal of Mathematics (2013), 261, 257-282.
  20. Simply Connected Spin Symplectic 4-Manifolds near Bogomolov-Miyaoka- Yau Line, with Park, B. D. & Urzua, G., Gokova Journal of Geometry and Topology. 2010, 55-66.
  21. Geography of Simply Connected Spin Symplectic 4-Manifolds, with B. D. Park, Math. Res. Letters, 17 (2010), no. 3, 483-492.
  22. Exotic Smooth Structures on Small 4-Manifolds with Odd Signatures , with D. Park (Invent. Math., 181 (2010), no. 3, 577-603).
  23. Simply connected minimal symplectic 4-manifolds with signature less than - 1, with Baldridge, S., Baykur, R. I., Kirk, P. and Park, B. D., Journal of the European Mathematical Society (2010) 12, 133-161.
  24. New Symplectic 4-Manifolds with Positive Signature, with B. D. Park, Journal of Gokova Geometry and Topology. 2008, p. 1-13
  25. Constructing Infinitely Many Smooth Structures on Small 4-Manifolds, with I. Baykur and B. D. Park, Journal of Topology, 2008, p. 409-428
  26. Exotic Smooth Structures on Small 4-Manifolds, with D. Park (Invent. Math., 173 (2008), no. 1, 209-223).
  27. Small Exotic 4-Manifolds, Algebraic and Geometric Topology (2008), no. 8, 1781-1794
  28. A Note on Stein Fillings of Contact Manifolds , with J. Etnyre, T. Mark, and I. Smith (Math. Res. Letters, 15 (2008), no. 6, 127-133).
  29. Construction of new symplectic cohomology S^2 x S^2, Proceedings of 14-th Gokova Geometry-Topology Conference 36-48 (2007)
  30. Construction of exotic smooth structures, Topology and its Applications (2007) no. 154, 1134-1140
  31. Surface bundles with non-zero signature, Topology and its Applications (2007), no. 154, 2235-2240

Slides from Conference and Seminar Talks

  • Exotic Lefschetz Fibrations and Stein Fillings with Arbitrary Fundamental Groups (at UMN, ESI (Vienna), UT Austin, Miami, Gokova)

  • Exotic Smooth Structures on 4-Manifolds (at UMN, Vienna, Stanford, Caltech, NDSU, MSU, Brandeis, UCI, Purdue, Columbia, Gokova, Zurich, Berkeley, Yale)

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