## Aleksey Zinger
## Department of Mathematics Stony Brook |
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- Counting genus zero real curves
in symplectic manifolds, Part II

joint with M. Farajzadeh Tehrani, math/1205.1809, 2 figures, Geom. Top. 20 (2016), no. 2, 629–695 - The moduli space of maps with crosscaps:
Fredholm theory and orientability

joint with P. Georgieva, math/1301.1074, 1 figure, Comm. Anal. Geom. 23 (2015), no. 3, 81–140 - The moduli space of maps with crosscaps:
the relative signs of the natural automorphisms

joint with P. Georgieva, math/1308.1345, J. Symplectic Geom. 14 (2016), no. 2, 359-430 - Orientability in real Gromov-Witten theory

joint with P. Georgieva, math/1308.1347, 25 pages, 3 figures - Enumeration of real curves in CP
^{2n-1}and a WDVV relation for real Gromov-Witten invariants

joint with P. Georgieva, math/1309.4079, 7 figures, 3 tables, Duke Math. 166 (2017), no. 17, 3291-3347 - A recursion for counts of real curves
in CP
^{2n-1}: another proof

joint with P. Georgieva, math/1401.1750, 3 figures, Internat. J. Math. 29 (2018), no. 4, 1850027, 21pp - Real Gromov-Witten theory in all genera
and real enumerative geometry: construction

joint with P. Georgieva, math/1504.06617, 48 pages, 5 figures, to appear in Ann. Math. 188 (2018), no. 3

Appendix computing one such invariant

Extended Abstract (for Penka's Oberwolfach talk): Oberwolfach Report 27/2006, 1643-1645 - Real Gromov-Witten theory in all genera
and real enumerative geometry: properties

joint with P. Georgieva, math/1507.06633, 55 pages, to appear in J. Symplectic Geom. - Real Gromov-Witten theory in all genera
and real enumerative geometry: computation

joint with P. Georgieva, math/1510.07568, 66 pages, 3 figures, to appear in J. Diff. Geom. - Lower bounds for enumerative counts
of positive-genus real curves

joint with J. Niu, math/1511.02206, 49 pages, 3 figures, 2 tables

Appendix computing low-genus low-degree real Gromov-Witten invariants

Jingchen's poster for AGNES, October 2015 - On the topology of real bundle pairs over nodal symmetric
surfaces

joint with P. Georgieva, math/1512.07216, 3 figures, Topology Appl. 214 (2016), 109-126 - Real orientations, real Gromov-Witten theory, and real
enumerative geometry

joint with P. Georgieva, math/1512.07220, ERA MS 24 (2017), 87–99 - Real Ruan-Tian perturbations

math/1701.01420, 50 pages, 2 figures

- Normal crossings singularities for symplectic topology

joint with M. Tehrani and M. McLean, math/1410.0609, 65 pages, 6 figures - The smoothability of normal crossings symplectic varieties

joint with M. Tehrani and M. McLean, math/1410.2573, 59 pages, 4 figures - Normal crossings degenerations of symplectic manifolds

joint with M. Tehrani, math/1603.07661, 65 pages, 2 figures - Singularities and semistable degenerations for symplectic topology

joint with M. Tehrani and M. McLean, math/1707.01464, 2 figures C. R. Math. Acad. Sci. Paris 356 (2018), no. 4, 420-432

- Pseudocycles and integral homology

math.AT/0605535, 2 figures, Trans. AMS 360 (2008), no. 5, 2741-2765

Older, more technical/direct version: math.AT/0605535v1, 37 pages, 3 figures - A comparison theorem for Gromov-Witten invariants
in the symplectic category

math/0807.0805, Adv. Math. 228 (2011), no. 1, 535--574 - On transverse triangulations

math/1012.3979, Munster J. Math. 5 (2012), 99-106 - The determinant line bundle for Fredholm operators:
construction, properties, and classification

math/1304.6368, Math. Scand. 118 (2016), no. 2, 203--268 - On symplectic sum formulas in Gromov-Witten theory (updated 12/28/14)

joint with M. Tehrani, 91 pages, 6 figures, math/1404.1898

Version from 03/14/14 (pre-arXiv); Updates 02/26/15; Related e-mails

Li-Ruan's arXiv response (with my comments in*red italics*in smaller print and at the end)

More on the Li-Ruan situation

Comments on Ionel-Parker's response - Absolute vs. relative Gromov-Witten invariants

joint with M. Tehrani, math/1405.2045, 46 pages, 11 figures, 4 tables, J. Symplectic Geometry, 14 (2016), no. 2, 1189-1250 - On the rim tori refinement of relative Gromov-Witten invariants

joint with M. Tehrani, math/1412.8204, 43 pages - On the refined symplectic sum formula
for Gromov-Witten invariants

joint with M. Tehrani, math/1412.8205, 54 pages - Notes on J-holomorphic maps

math/1706.00331, 52 pages, 11 figures

- Genus-zero two-point hyperplane integrals
in the Gromov-Witten theory

math/0705.2725, 4 figures, Comm. Anal. Geom. 17 (2010), no. 5, 1-45 - The reduced genus-one Gromov-Witten
invariants of Calabi-Yau hypersurfaces

math/0705.2397, 5 figures, JAMS 22 (2009), no. 3, 691-737 - Some properties of hypergeometric series associated
with mirror symmetry

joint with D. Zagier, math/0710.0889,*Modular Forms and String Duality*, Fields Inst. Commun. 54 (2008), 163-177 - Mirror formulas for closed, open, and unoriented
Gromov-Witten invariants

joint with A. Popa, math/1010.1946, 2 figures, 5 tables, Adv. Math. 259 (2014), 448-510 - The genus 0 Gromov-Witten invariants of
projective complete intersections

math/1106.1633, 3 fugures, 4 tables, Geom. Top. 18 (2014), no. 2, 1035-1114 - Mirror symmetry for stable quotients invariants

joint with Y. Cooper, math/1201.6350, 6 figures, 1 table, Mich. Math. J. 63 (2014), no. 3, 571–621 - Double and triple Givental's J-functions for
stable quotients invariants

math/1305.2142, 9 figures, 1 table, Pacific J. Math. 272 (2014), no. 2, 439–507 - Energy bounds and vanishing results for
the Gromov-Witten invariants of the projective space

math/1801.07242, 57 pages, 4 figures - Equivariant Localization and Mirror Symmetry

course notes inspired by Pandharipande's notes on Givental's proof of mirror symmetry for the quintic, in preparation whenever I teach this course; Chapters 1 and 4 and the beginning of Chapter 2 should be complete, but there is not much beyond that

- A sharp compactness theorem for genus-one
pseudo-holomorphic maps

math.SG/0406103, 7 figures, Geom. Top. 13 (2009), no. 5, 2427-2522

Some comments, 2 pages - On the structure of certain natural cones over moduli
spaces of genus-one holomorphic maps

math.SG/0406104, 3 figures, Adv. Math. 214 (2007), no. 2, 878–933 - On the genus-one Gromov-Witten invariants
of a quintic threefold

joint with J. Li, math.AG/0406105, 5 figures, Pacific J. Math 233 (2007), no. 2, 417-480 - Reduced genus-one Gromov-Witten invariants

math.SG/0507103, 5 figures, JDG 83 (2009), no. 2, 407-460 - On the genus-one Gromov-Witten invariants of
complete intersections

joint with J. Li, math.AG/0507104, 4 figures, 1 table, JDG 82 (2009), no. 3, 641-690 - A desingularization of the main component of
the moduli space of genus-one stable maps into P
^{n}

joint with R. Vakil, math.AG/0603353, 13 figures, Geom. Top. 12 (2008), 1-95

Overview (independent): 2 figures, ERA AMS 13 (2007), 53-59

Extended Abstract (for Ravi's Oberwolfach talk): Oberwolfach Reports 27/2006, 1643-1645 - Intersections of tautological classes on
blowups of moduli spaces of genus-one curves

math.AG/0603357, 5 figures, Mich. Math. 55 (2007), no 3, 535-560 - Standard vs. reduced genus-one Gromov-Witten invariants

math/0706.0715, Geom. Top. 12 (2008), no. 2, 1203-1241

- Completion of Katz-Qin-Ruan's enumeration of genus-two
plane curves

math.AG/0201216, 3 figures, 1 table, J. Algebraic Geom. 13 (2004), no. 3, 547-561 - Enumerative vs. symplectic invariants
and obstruction bundles

math.SG/0201255, J. Symplectic Geom. 2 (2004), no. 4, 445--543 - Enumeration of genus-two curves with a fixed
complex structure in P
^{2}and P^{3}

math.SG/0201254, 2 figures, 3 tables, J. Diff. Geom. 65 (2003), no. 3, 341-467 - Enumeration of genus-three plane curves with
a fixed complex structure

math.SG/0203058, 3 tables, J. Algebraic Geom. 14 (2005), no. 1, 35-81 - Enumeration of one-nodal rational curves
in projective spaces

math.AG/0204236, 9 figures, 1 table, Topology 43 (2004), no. 4, 793-829 - Counting rational curves of arbitrary shape
in projective spaces

math.AG/0210146, 15 figures, 5 tables, Geom. Top. 9 (2005), 571-697 - Enumerative geometry of Calabi-Yau 5-folds

joint with R. Pandharipande, math/0802.1640, 6 figures, 3 tables,*New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry*, ASPM 59 (2010), 239-288

Appendix (self-contained), 6 pages

- The exponential decay rate of the lower bound for
the first eigenvalue of compact manifolds

joint with M. Kalka, E. Mann, and D. Yang, 1 figure, Internat. J. Math. 8 (1997), no. 3, 345--355 -
Enumerative algebraic geometry via techniques of
symplectic topology and analysis of local obstructions

Ph.D. Thesis, MIT 2002, 240 pages, 8 tables - Counting plane rational curves: old and new approaches

math.AG/0507105, expository notes, 32 pages, 2 figures, 2 tables - Basic Riemannian geometry and Sobolev estimates
used in symplectic topology

math/1012.3980, expository notes, 33 pages, 3 figures - On the robustness of extortionate strategies
in iterated Prisoner's Dilemma

joint with J. Chen, 5 figures, 6 tables, J. Theor. Bio., 357 (2014), 46–54 - Some conjectures on
the asymptotic behavior of Gromov-Witten invariants

math/1610.02971, 26 pages, 1 figure; old version - Some questions in the theory of pseudoholomorphic curves

math/1805.09647, 28 pages, 4 figures - Foundations of Smooth Manifolds and Vector Bundles

course notes inspired by Warner's book, in preparation whenever I teach this course; the first two chapters should be complete, but there is not much beyond that

This page is maintained by Aleksey Zinger.