# Pierre Deligne

## Belgio/USA

### Premio Balzan 2004 per la matematica

#### Progetto di ricerca

**The Pierre Deligne Contest**

Pierre Deligne is a Professor at the Institute for Advanced Study in Princeton NJ. He used the second half of his Balzan Prize to sponsor a competition for young mathematicians of Russia, Ukraine and Belarus. The Pierre Deligne Contest had the aim of helping young mathematicians to stay in their home countries to carry out scientific research. The contest winner was awarded a three-year research grant.

Any person 35 or under who had a PhD in mathematics and lived in Russia, Ukraine or Belarus was eligible for the competition. Competitors had to provide a research statement, and grant recipients had to present an annual report with a summary of that year’s achievements and their plans for the following year. All papers submitted by grant recipients during the grant period were to mention partial funding from Pierre Deligne’s 2004 Balzan Prize in Mathematics.

Balzan funds were used to finance seventeen three-year research grants: five in December 2005; five in 2006; five in 2007; two in 2008. Since the grants were for three years, those awarded in 2008 continued until the end of 2011. Even though the funds were exhausted after the 2008 round, Pierre Deligne found the resources to prolong the awarding of grants through 2009.

Afterwards, the competition was continued by the Dynasty Foundation (Russia), until the demise of this Foundation in 2015.

**Publications**

The project resulted in over seventy publications.

**Ivan Arzhantsev**

Arzhantsev IV. 2009. On the factoriality of Cox rings. Mat. Zametki. 85, no. 5: 643-651.

Arzhantsev IV. 2009. Projective embeddings with a small boundary for homogeneous spaces. Izv. Ross. Akad. Nauk Ser. Mat. 73, no. 3: 5-22.

Arzhantsev IV, Gaifullin S. 2010. Cox rings, semi groups and automorphisms of affine varieties. Sbornik Math. 201, no. 1: 3-24.

**Mikhail Bondarko**

Bondarko MV. 2007. Canonical representatives in strict isomorphism classes of formal groups. Mathematical Notes. v. 82, n. 1-2: 159-164.

Bondarko MV, Dievsky AV. Non-abelian associated orders of wildly ramified local field extensions. 2008. Zapiski Nauchnyh Seminarov POMI. vol. 356: 5-45.

Bondarko MV. 2009. Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura. J. Inst. Math. of Jussieu. 8, no. 1: 39-97.

Bondarko MV. 2010. Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general). Journal of K-theory. Vol. 6, 03: 387-504.

**Denis Borisov**

Borisov D. On the spectrum of two quantum layers coupled by a window. 2007. Journal of Physics A: Mathematical and Theoretical. V. 40. No. 19: 5045-5066.

Borisov D. 2007. Asymptotic behavior of the spectrum of a waveguide with distant perturbation. Mathematical Physics, Analysis and Geometry. V. 10. No. 2: 155-196.

Borisov D. 2007. Distant perturbations of the Laplacian in a multi-dimensional space. Annales Henri Poincare. V. 8. No. 7: 1371-1399.

Borisov D, 2008.Gagilishin R. Spectrum of periodic operators with a small local perturbation. Izv. T.72, 4: 37-66.

Borisov D. 2008. Asymptoties of solutions of ellipti systems with rapidly oscillating coefficients. Alg. i An. 20: 19-42.

Borisov D, Krejcirik D. 2008. PT-symmetric waveguide. Integral Equations and Operator Theory. V. 62. No. 4: 489-515.

Borisov D, Cardone G. 2009. Homogenization of the planar waveguide with frequently alternating boundary conditions. Journal of Physics A: Mathematics and General. V. 42. No. 36, 365205 (21pp).

Borisov D, Freitas P. 2009. Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Journal of Differential Equations (2009), V. 247. No.11: 3028-3039.

Borisov D, Freitas P. 2009. Singular asymptotic expansions for Dirichlet eigenvalues andeigen functions on thin planar domains. Annales de l’Institut Henri Poincare (C) Analyse non-lineaire. V. 26. No. 2: 547-560.

Borisov D, Freitas P. 2010. Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in Rd. Journal of Functional Analysis. 258 3: 893-912.

**Evgenii Feigin**

Feigin B, Feigin E, Jimbo M, Miwa T, Takeyama Y. 2008. A φ1,3-Filtration of the Virasoro Minimal Series M (p, ?) with 1 < ?/p < 2. Publ. Res. Inst. Math. Sci. Volume 44, Number 2: 213-257.

Feigin E. 2009. N = 1 formal genus 0 Gromov-Witten theories and Givental’s formalism. Journal of Geometry and Physics. 59 (2009): 1127-1136.

Feigin B, Feigin E, Jimbo M, Miwa T, Mukhin E. 2009. Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian. Letters in Mathematical Physics: Volume 88, Issue 1: 39-77.

**Pavel Kolesnikov**

Kolesnikov P. 2006. Identities of conformal algebras and pseudoalgebras. Comm. Algebra. 34, no. 6: 1965-1979.

Kolesnikov P. 2007. On the Wedderburn principal theorem in conformal algebras, J. Algebra and Its Appl., 6, no. 1: 119-134.

Kolesnikov P. 2008. Associative algebras related to conformal algebras. Applied Categorical Structures16. no. 1-2: 167-181.

Kolesnikov P. 2008. Universally defined representations of conformal Lie superalgebras. Journal of Symbolic Computation 43, no. 6-7: 406-421.

Kolesnikov P. 2008. On Irreducible subalgebras of matrix Weyl algebras. Shum KP et al., editors. Advances in Algebra and Combinatorics, 205-217. Hong Kong: World Scientific Publishing Co.

Kolesnikov P. 2008. On irreducible algebras of conformal endomorphisms over a linear algebraic group. Sovrem. Mat. Prilozh T60: 42-56.

Kolesnikov P. 2009. Conformal Algebras in The Context of Linear Algebraic Groups. Silvestrov S et al., editors. Generalized Lie Theory in Mathematics, Physics and Beyond, 235-246. Berlin: Springer.

**Alexander Kuznetsov**

Kuznetsov A. 2006. Hyperplane sections and derived categories. Izvestiya RAN: Ser. Mat. pp. 23-128 (in Russian); translation in Izvestiya: Mathematics. 70:3 (2006): 447-547.

Kuznetsov A. 2007. Homological projective duality. Publ. Math. IHES. 105, n. 1: 157-220.

Kuznetsov A. 2007. Quiver varieties and Hilbert schemes. Moscow Mathematical Journal. Volume 7, N. 4.

Kuznetsov A. 2008. Derived categories of quadric fibrations and intersections of quadrics. Advances in Mathematics, V. 218, N. 5: 1340-1369.

Kuznetsov A. 2008. Exceptional collections for Grassmannians of isotropic lines. Proceedings of the London Mathematical Society, V. 97, N. 1: 155-182.

Kuznetsov A. 2008. Lefschetz decompositions and categorical resolutions of singularities. Selecta Mathematica. V. 13, N. 4: 661-696.

Kuznetsov A. 2008. Derived categories and rationality of cubic fourfolds. Proceedings of the 5th European Congress of Mathematics, Amsterdam.

**Sergey Loktev**

Etingof P, Loktev S, Oblomkov A, Rybnikov L.2008. A Lie-theoretic construction of spherical symplectic reflection algebras. Transformation Groups. 13, no. 3: 541-556.

Guay N, Hernendez D, Loktev S. 2009. Double affine Lie algebras and finite groups. Pacific Math. J. 243, no. 1: 1-41.

Loktev S. 2010. Weight Multiplicity Polynomials of multi-variable Weyl Modules. Moscow Math. J. 10 1: 215-229.

**Taras Panov**

Maeda H, Masuda M, Panov T. 2007. Torus graphs and simplicial posets. Advances in Mathematics. 212, no. 2: 458-483.

Buchstaber VM, Panov TE, Ray N. 2007. Spaces of polytopes and cobordism of quasitoric manifolds. Moscow Mathematical Journal. 7, no. 2: 219-242.

Panov T. 2008. Cohomology of face rings, and torus actions, in Surveys in Contemporary Mathematics. London Math. Soc. Lecture Note Series. Cambridge, U.K. vol. 347: 165-201.

Masuda M, Panov T. 2008. Semifree circle actions, Bott towers, and quasitoric Manifolds. Mat. Sb.199, no. 8: 95-122.

Panov T, Ray N. 2008. Categorical aspects of toric topology. Harada M et al. editors, Toric Topology s. Contemp. Math. vol. 460: 293-322. Providence (RI): Amer. Math. Soc. Panov T. 2008. Toric Kempf-Ness sets. Proc. Steklov Inst. Math. vol. 263: 159-172.

**Marat Rovinski**

Rovinsky M. 2005. Motives and admissible representations of automorphism groups of fields. Math. Zeit. 249, no. 1: 163-221.

Rovinsky M. 2005. Semilinear representations of PGL. Selecta Math. 11: 491-522.

Rovinsky M. 2007. Admissible semi-linear representations. J. Reine Angew. Math. 604: 159-186.

Rovinsky M. 2007. Automorphism groups of fields, and their representations. Russian Math. Surveys, 62:6 (2007): 1121-1186.

Rovinsky M. 2009. On maximal proper subgroups of field automorphism groups. Selecta Math. 15: 2 (2009): 343-376.

**Leonid Rybnikov**

Chervov A, Falqui G, Rybnikov L. 2009. Limits of Gaudin Systems: Classical and Quantum Cases. SIGMA 5, 029, 17 pages.

**Anton Savin**

Nazaikinskii VE, Savin AYu, Sternin BYu. 2008. Noncommutative geometry and the classification of elliptic operators (in Russian). Sovrem Mat. Fundam. Napravl. 29: 131-164.

Nazaikinskii E, Savin AYu, Sternin BYu. 2008. Elliptic theory and noncommutative geometry. Operator Theory: Advances and Applications, volume 183. Basel: Birkhäuser Verlag.

Nazaikinskii E, Savin AYu, Sternin BYu. 2008. On index of non local elliptic operators. Dokl. 420 5 (2008).

Nazaikinskii E, Savin AYu, Sternin BYu. 2008. Non commutative geometry and classification of elliptic operators. Sovrem Mat. Fundam Napravl. 29 1:131-169.

Nazaikinskii VE, Savin AYu, Sternin BYu. 2009. On the Poincaré isomorphism in Ktheory on manifolds with boundaries (in Russian). Sovrem. Mat. Fundam. Napravl. 34 (2009), 109-120.

Nazaikinskii VE, Savin AYu, Sternin BYu. The Atiyah-Bott index on stratified Manifolds (in Russian). Sovrem. Mat. Fundam. Napravl. 34 (2009), 100-108.

Savin AYu, Sternin BYu. 2009. Surgery and index formulas on stratified manifolds (inRussian), Dokl. Akad. Nauk 427, no. 3: 313-317. 163

Savin AYu, Sternin BYu. 2009. The index of nonlocal elliptic operators over C*-algebras (in Russian) Dokl. Akad. Nauk. 426, no. 3: 314-317.

Nazaikinskii E, Savin A, Sternin B. 2009. Atiyah-Bott index on stratified varieties. Sovrem Mat. Fundam Napravl. 34: 100-108.

Savin AYu, Sternin BYu. 2010. Non local elliptic operators on compact Lie groups. Dokl. Nauk.

**Ilya Shkredov**

Shkredov I. 2009. On sumsets of dissociated sets. Online J. of Anal. Comb. 4, Art. 4, 26 pp. Shkredov I. 2009. On an inverse theorem for U3(_)-norm, Modern problems of mathematics and mechanics, Mathematics, Dynamical systems. v. 4, 2: 55-127.

Shkredov I. 2011. Some applications of W. Rudins inequality to problems of combinatorial number theory. Uniform Distribution Theory. Volume: 6; Issue: 2: 95-116.

**Arcady Skopenkov**

Skopenkov A. 2007. A new invariant and parametric connected sum of embeddings. Fund. Math. 197: 253-269.

Skopenkov A. 2007. A characterization of submanifolds by a homogeneity condition.Topol. Appl. 154 (2007), 1894-1897.

Cencelj M, Repovs D, Skopenkov A. 2007. Codimension two PL embeddings of spheres with nonstandard regular neighborhoods. Chinese Annals of Mathematics, Series B. 28:5: 603-608.

Skopenkov A. 2008. Classification of smooth embeddings of 3-manifolds in 6-space. Math. Zeitschrift. 260:3, (2008): 647-672.

Skopenkov A. 2008. Embedding and knotting of manifolds in Euclidean spaces. Young N, Choi Y, editors, Surveys in Contemporary Mathematics. London Math. Soc. Lect. Notes. 347: 248-342.

**Evgenii Vdovin**

Vdovin EP. 2009. Carter subgroups of finite groups. Siberian Adv. Math. v. 19, No. 1: 1-15.

**Link:**

http://www.mccme.ru/pdc/rules_e.html

Excerpt from the: The Balzan Prizewinners’ Research Projects: An Overview 2016

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