Vladimir Chernov (Tchernov)

Curriculum Vitae
 
 
 

Department of Mathematics

6188 Kemeny Hall

Tel: +1-(603) 646 24 21

Fax: +1-(603) 646 13 12

E-mail: Vladimir.Chernov@dartmouth.edu

Dartmouth College

Hanover, NH 03755-3551, USA

 

 

 

 

 

 

 

 

 

 

Personal Information

Previous spelling of the last name: Tchernov
Birth date: January 9, 1972
Citizenship: Russian citizen, US permanent resident

Research Interests

·        Contact and Symplectic Topology, specifically:  Legendrian and transverse knots (57R17) and their relations to wave front propagation (78A05); Bennequin-type inequalities; Legendrian and Lagrangian immersions and embeddings.

·        Geometric and Low-Dimensional Topology, specifically: knots and links in manifolds (57M27); Vassiliev invariants of knots; invariants of immersed curves and surfaces; higher dimensional link theory  (57Q45); generalized linking numbers.

·        Algebraic Topology and Global Analysis, specifically: spaces of imbeddings and immersions (58D10) and their homotopy groups; manifolds of mappings (58D15).

·        Interactions between link theory, Lorentz manifolds (53C50), contact and symplectic topology, and mathematical physics. Specifically: relations between causality and linking in strongly causal and globally hyperbolic spacetimes  (83C75); nonrefocussing spacetimes; Legendrian and Lagrangian submanifolds in manifolds of geodesics for semi-Riemannian manifolds.

Degrees

(Because my scientific advisor held positions at both Universities, I had to enroll into Graduate Programs at both places and to defend Ph.D.s at both places. The theses for the two Ph.D.s are based on different material.)

·         Licentiate in Mathematics. Uppsala University, 1996

·         Diploma in Mathematics. St. Petersburg State University, Russia, 1996

·         M.Sci. in Mathematics. University of California at Riverside (UCR), 1994

Academic Positions

  1. Dartmouth College, Mathematics Department. Summer 2007 - Now Associate Professor, Summer 2001 – Summer 2007 Assistant Professor.
  2. Zurich University, Mathematics Department. Fall 2000 - Summer 2001. Postdoc
  3. Max-Planck-Institut fur Mathematik, Bonn. Fall 1999 - Summer 2000. Scientific Visitor for one year.
  4. ETH Zurich. Fall 1998 - Summer 1999. Postdoc.

 

Teaching the following Dartmouth courses

·  Math 8 Calculus of one and several variables Spring 2002;

·  Math 9 Multivariable Calculus (Honors) Fall 2001, Fall 2002, Fall 2003;

·  Math 11 Calculus for First-Year Students with two terms of AP credit, Fall 2004;

·  Math 12 Calculus Plus, Fall 2007; Fall 2009; Fall 2012

·  Math 13 Calculus of Vector Valued Functions Winter 2004; Winter 2008; Fall 2011;

·  Math 14  Calculus of Vector Valued Functions Winter 2002, Winter 2003, Winter 2011;

·  Math 23 Differential Equations Spring 2002, Winter 2006; Spring 2009; Fall 2010; Fall 2011; Fall 2012;

·  Math 31 Topics in Algebra Winter 2004;

·  Math 35 Real Analysis Winter 2007;

·  Math 43 Functions of a Complex Variable Spring 2007;

·  Math 46 Introduction to Applied Mathematics Spring 2010;

·  Math 63 Real Analysis Winter 2009;

·  Math 73 Multi-Variable Analysis Winter 2003;

·  Math 103, Topics in Analysis Fall 2004, Fall 2005; Fall 2007; Fall 2009;

·  Math 104 Topics in Topology Winter 2009;

·  Math 124 Current Problems in Topology Fall 2002; Fall 2003; Fall 2005; Fall 2010; Winter 2012.

 

 

Former Ph.D. Students: 

 

1.      Allison Henrich Ph.D. 2008, Title of the Ph.D. Thesis “A sequence of degree one Vassiliev invariants for virtual knots” Currently a tenure track Assistant Professor at Seattle University

2.      Paul Kinlaw Ph.D. 2010, Title of the Ph.D. Thesis: “Refocusing of null geodesics in Lorentz manifolds” Currently an Assistant Professor at Husson University

3.      Patricia Cahn, Ph. D. (2012) Ph. D. Thesis TItle: \Algebras counting self-intersections of curves." Currently a Lecture of Mathematics at the University of Pennsylvania.

Current Ph.D. Students: 

1.     Asa Levi

 

Grants:  A five year “Collaboration Grants for Mathematicians” from the Simons Foundation awarded in 2012, award number 235674. Grant amount $35000. Project title: “Causality and Legendrian Linking”.

 

 

Works submitted for publication

1.     V. Chernov: “Some Corollaries of Manturov's Projection Theorem”, preprint arXiv:1209.0178 at www.arxiv.org submitted for publication, 5 pages (2012)

2.     V. Chernov, S. Nemirovski: “Smooth cosmic censorship”, preprint arXiv:1201.6070 at www.arxiv.org submitted for publication, 4 pages (2012)

Published and Accepted Refereed Research Publications

1. P. Cahn, V. Chernov: “Intersections of Loops and the Andersen-Mattes-Reshetikhin Algebra”, preprint arXiv:1105.4638 at www.arxiv.org,to appear in the Journal of the London Mathematical Society 19 pages (2011)

2.     V. Chernov and S. Nemirovski: "Non-negative Legendrian isotopy in ST*M", published in Geometry and Topology 14, no. 1 (2010) 611-626

3.     V. Chernov and S. Nemirovski: “Legendrian links causality and the Low conjecture”  published in GAFA (Geometric and Functional Analysis) 19, no. 5, (2010) 1320-1333

4.     V. Chernov, P. Kinlaw and R. Sadykov: “Topological properties of manifolds admitting a Yx-Riemannian metric”  published in J. Geom. Phys. 60, no. 10 (2010) 1530-1538

5.     V. Chernov (Tchernov) and Yu. Rudyak: “On generalized Winding Numbers” published in Algebra i Analysis 20 no. 5, (2008),  217 – 233

6.     E. Byberi and V. Chernov (Tchernov): “Virtual Bridge Number One Knots” published in Communications in Contemporary Mathematics,   10  (2008),  suppl. 1, 1013-1021

7.     V. Chernov (Tchernov) and Yu. Rudyak: "Linking and Causality in Globally Hyperbolic Space-times" published in Communications in Mathematical Physics, 279, no 2, (2008) pages 309-354

8.     V. Chernov (Tchernov): "Mapped Null Hypersurfaces and Legendrian Maps", published in  Journal of Geometry and Physics  57, no 10, (2007) pages 2114-2123

9.     V. Chernov (Tchernov),Yu. Rudyak: “Toward a General Theory of Linking Invariants”, published in Geometry and Topology Vol. 9 (2005) Paper no. 42, pages 1881-1913

10.     V Chernov (Tchernov): “Framed Knots in 3-manifolds and affine self-linking numbers” published at J. Knot Theory Ramifications  14 (2005) no. 6, pages791-819

11.   V Chernov (Tchernov): “Relative Framing of Transverse knots”,  published in Int. Math. Res. Not. Issue 52 (2004) 2773-2797

12.   V Chernov (Tchernov): “The universal order one invariant of framed knots in most S1-bundles over orientable surfaces”,  Algebraic and Geometric Topology  Vol. 3 (2003) pp. 89-101

13.   V. Tchernov (Chernov): “Isomorphism of the groups of Vassiliev Invariants of Legendrian and of pseudo Legendrian knots” Compositio Math. 135 (2003), no. 1, 103-122.

14.  V. Tchernov (Chernov): “Vassiliev invariants of Legendrian, transverse, and framed knots in contact three-manifolds”. Topology 42 (2003), no. 1, 1-33.

15.   A. Stoimenow, V. Tchernov (Chernov), A. Vdovina: “The canonical genus of a classical and virtual knot”, MPI preprint 108 (2000) Geom. Dedicata 95 (2002), 215-225.

16.   V. Tchernov (Chernov): “Arnold-type invariants of wave fronts on surfaces” Topology 41 (2002), no. 1, 1-45

17.   V. Tchernov (Chernov): “Homotopy groups of the space of curves on a surface”. Math. Scand. 86 (2000), no. 1, 36-44.

18.   V. Tchernov (Chernov): “Arnold-type Invariants of Curves on Surfaces”, J. Knot Theory Ramifications 8 (1999), no. 1, 71-97.

19.  V. Tchernov (Chernov): “Shadows of wave fronts and Arnold-Bennequin type invariants of fronts on surfaces and orbifolds.” Differential and symplectic topology of knots and curves, 153-184, Amer. Math.

Soc. Transl. Ser. 2, 190, Amer. Math. Soc., Providence, RI, (1999). There is no electronic version of this publication. The corresponding arXiv preprint is math.GT/9906121.

20.  V. Tchernov (Chernov): “The most refined Vassiliev invariant of degree one of knots and links in R1-fibrations over a surface.” J. Knot Theory Ramifications 7 (1998),  no. 2, pages 257-266.

 

 Minicourses

1.     A  three lecture minicourse ``Causality and Legendrian Linking'' at the VI International Meeting on Lorentzian Geometry, Granada Spain, September 6-9, 2011

 

Talks at Conferences and Seminars (talk titles and dates are provided when available)

 

1.     A talk “Smooth Cosmic Censorship and determining causality from linking” on August 20 at the “Fourth Geometry Meeting dedicated to the centenary of A.D.Alexandrov”  held at the Euler International Mathematical Institute held August 20-25, 2012

2.     A talk “Cosmic censorship of smooth structures and integer valued metrics on spacetimes” on August 8, 2012 at the “Geometric Topology” Seminar of the Steklov Mathematical Institute, Moscow Russia

3.     A talk “Legendrian linking and causal structure in a spacetime” on March 24  at the “46th Annual Spring Topology and Dynamics Conference” held at Universidad Nacional Autonoma de Mexico (UNAM) Mexico City, Mexico, March 22-24, 2012

4.     A Colloquium talk “Smooth Cosmic Censorship and determining causality from linking” on March 21, 2012 at the Depto. de Matemáticas,   CINVESTAV, Mexico City, Mexico

5.      A talk “Computing causal relation between events from the set of points where the events are visible at a given time moment” on March 17 at the “Special Session on Mathematics Applied in the Sciences: From Statistics to Topology” session of the 2012 Spring Eastern Sectional Meeting #1080 held at the George Washington University, Washington, DC March 17-18, 2012

6.     A talk “Smooth Cosmic Censorship” on March 15 at the XXXIV Knots in Washington Conference held at George Washington University, Washington DC, March 14-16, 2012

7.     An invited one hour talk “Low conjecture, linking and causality in global hyperbolic Lorentz spacetimes'” on June 16 at the The 87th Encounter between Mathematicians and Theoretical Physicists “Lorentz geometry in Mathematics and in Physics” dedicated to Norbert A Campo for his 70th birthday, June 16-18, 2011

8.     A talk “Causality in spacetimes and Legendrian linking” on March 17, 2011 at the Thursday Seminar on Topology, at SUNY Stony Brook

9.     A talk ``Causality, Low Conjecture and globally hyperbolic spacetimes" on February 15, 2011 at the Topology Seminar, Brandeis University

  1. A talk “Causality, Low conjecture and the partial order on the space of Legendrian spheres” on November 19, 2010 at the Analysis-Geometry Seminar, Northeastern University
  2. A talk “Causality, Low conjecture and the partial order on the space of Legendrian spheres” on September 24, 2010 at the Gauge Theory and Topology Seminar, Harvard University
  3. A talk “Algebras detecting minimal intersection and self intersection numbers of curves on a surface” on September 15, 2010 at the Geometry Luncheon Seminar, Penn State University, State College, PA
  4. A talk “Legendrian linking, refocussing and causality in spacetimes” on September 15, 2010 at the Center for Dynamics and Geometry Seminar, Penn State University, State College, PA
  5. A talk “Causality in space-times, Low conjecture and the partial order on Legendrian spheres” on August 18, 2010 at the International Conference “Geometry, Topology, Algebra and Number Theory, Applications” dedicated to the 120th anniversary of Boris Delone, Steklov Mathematical Institute, Moscow, Russia
  6. A talk “Refocussing and Yx -manifolds” on June 18, 2010 at the Moscow - St Petersburg

seminar of Low-dimensional Mathematics, POMI, St Petersburg, Russia

  1. A talk “Topological Properties of Manifolds admitting a Yx-Riemannian metric” on January 26, 2010 at the Analysis seminar of the Department of Mathematics, University of Western Ontario, London, Canada
  2.  A Colloquium talk “Legendrian links, causality, and the Low conjecture” on January 28, 2010 at the Department of Mathematics, University of Western Ontario, London, Canada
  3.  An invited talk “Legendrian links, causality, and the Low conjecture” on October 30, at the special session on Geometry and Topology of the 2009 Fall Southeastern AMS Sectional #1053 Meeting held in Boca Raton, Florida on October 30-November 1, 2009
  4.  A talk “Legendrian links, causality, and the Low conjecture” at the seminar "Mnogoobraziya i ih otobrazheniya" (“Manifolds and their mappings”) at the Mechanics and Mathematics Department of the Moscow State University, Moscow, Russia on September 11, 2009
  5.  A talk “Legendrian links, causality, and the Low conjecture” at the D. Sokolov seminar "Cosmic electrodynamics and dynamo theory" at the “Research Computing Center” of the Moscow State University, Moscow, Russia on September 10, 2009
  6.  A talk “Legendrian links, causality, and the Low conjecture” at the symplectic geometry seminar of the Department of Mathematics, Columbia University, on April 24, 2009
  7.  A talk “Linking, Causality and Refocusing” at the “Rokhlin Topology Seminar” at the St. Petersburg Department of the Steklov Institute of Mathematics, St Petersburg, Russia, on September 8, 2008
  8.  A talk “Linking, Causality and Refocusing” at E. A. Kudryavtseva and S. A. Bogatyi seminar "Mnogoobraziya i ih otobrazheniya" (“Manifolds and their mappings”) at the Mechanics and Mathematics Department of the Moscow State University, Moscow, Russia on September 4, 2008
  9.  A talk “Selflinking invariant for nonzerohomologous framed knots in 3-manifolds” at the Shepin Topology seminar at the Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia on September 3, 2008
  10.  A talk “Vassiliev invariant estimates for unknotting numbers of virtual knots.” at the V. Manturov “Knots and Representation Theory” at the Mechanics and Mathematics Department of the Moscow State University, Moscow, Russia on September 2, 2008
  11.  A talk “Linking of skies and causality in globally hyperbolic spacetimes” on July 3, 2008 at the “Differential Geometry and General Relativity” section of the Fifth World Congress of Nonlinear Analysts held July 2-9 in Orlando, Florida
  12.  A talk “Linking of skies and causality in globally hyperbolic spacetimes”  at the Topology Seminar of the University of Tennessee, Knoxville on April 4, 2008
  13.  An invited talk “Causality and linking in space-times” on February 24 at the Texas Geometry and Topology Conference, held February 22-24, 2008 at the Texas Tech University, Lubbock, Texas
  14.  A talk “Causality, linking and refocussing space-times” on September 14 at the “Algebra and Geometry Around Knots and Braids” conference, held September 10-14, 2007 in the Euler Institute, St Petersburg, Russia
  15.  A talk “Linking and causality in globally hyperbolic spacetimes'' on August 21 at the ``Analysis and singularities'' conference, held August 20-24, 2007 in the Steklov Mathematical Institute,
  16.  A talk “Garlands, graded Poisson algebras, and applications.” at the “Topology and Dynamical Systems Seminar”, University of Florida, Gainesville, March 20, 2007
  17.  A talk “Some applications of the Graded Poisson algebras on bordism groups of garlands” at the Topology Seminar, Mathematics Department, Ohio State University, October 31, 2006
  18.  An invited talk “Poisson and other algebras on bordism groups of garlands.” on October 29 (2006) at the “Special Session on Homotopy Theory of Compactified Moduli Spaces” at the AMS 2006 Fall Eastern Section #1021 Meeting Storrs, CT, held October 28-29, 2006
  19.  A talk "Graded Poisson algebras, bordism groups, affine linking numbers and applications." at the Gauge Theory and Topology Seminar, Department of Mathematics, Harvard University, October 20, 2006
  20.  A talk "Graded Poisson algebras on bordism groups of garlands and minimizing intersection of loops on a surface." at the Topology Seminar, Mathematics Department, Brandeis University, October 17, 2006
  21.  An invited talk "Graded Poisson algebras on bordism groups of odd-dimensional garlands and minimizing the intersection of loops on a surface." on October 8 (2006) at the "Special Session on Floer Methods in Low-dimensional Topology" of the AMS  2006 Fall Western Section Meeting #1019, Salt Lake City, UT, held October 7-8, 2006
  22.  A talk "Graded Poisson algebras on bordism groups of garlands."at the “Rokhlin Topology Seminar”, at the St. Petersburg Department of the Steklov Institute of Mathematics, St Petersburg, Russia, September 11, 2006
  23.  A talk "Applications of the Ω*-algebra of the space of garlands." on June 9 2006 at the Lehigh University Geometry and Topology Conference, held June 8-10, 2006
  24.  A talk "Generalized strings algebra." at the Geometry and Topology seminar, Department of Mathematics and Statistics, University of Calgary, Canada, May 10, 2006
  25.  Colloquium talk "Affine linking numbers and their applications to the study of wave front propagation." Department of Mathematics and Statistics, University of Calgary, Canada, May 5, 2006
  26.  A talk "Relative framing of transverse knots." at the Symplectic Topology Seminar, Department of Mathematics and Statistics, University of Calgary, Canada, May 1, 2006
  27.  A talk "New algebraic structures on the generalized string algebra." on December 4 2005 at the “Algebraic Topology” section of the Union College Mathematics Conference, Union College, Schenectady NY, held December 3-4, 2005
  28.  A talk "Framed knots in 3-manifolds and affine self-linking numbers." at the “Rokhlin Topology Seminar”, Steklov Institute of Mathematics at St Petersburg, Russia, September 12, 2005
  29.  A talk "Relative framings of transverse knots." at the “Moscow-Petersburg Seminar on Low-Dimensional Mathematics”, Steklov Institute of Mathematics at St Petersburg, Russia, September 9, 2005
  30.  A talk "Generalizations of Chas-Sullivan string homology and applications to link and coincidence theories." on July 26 2005 at the 5 International Siegen Topology Symposium “Manifolds and Their mappings” held at Siegen University, Germany, on July 25-29, 2005
  31.  A talk "Relative framing of transverse knots and Vassiliev invariants of transverse and pseudo-Legendrian knots." on June 5 2005 at the AMS-IMS-SIAM Summer Research Conference "Quantum Topology-Contemporary Issues and Perspectives" held at Snowbird Utah, June 5-9, 2005
  32.  A talk "Relative framing of transverse knots." on November 7 2004 at the “Special Session on Invariants of knots and 3-manifolds” of the 2004 Fall Eastern Section Meeting of the AMS #1042, Pittsburgh, PA, November 6-7, 2004
  33.  A talk "Algebraic structures on generalized string and applications." at the Differential Geometry and Topology Seminar of the Universite du Quebec a Montreal, Montreal, Canada, September 17, 2004
  34.  A talk "Relative framings of transverse knots." on August 26 2004 at the “L.V. Keldysh Centennial Conference in Geometric Topology, Discrete Geometry and Set Theory”  held August 24-28 at the Steklov Mathematics Institute of the Russian Academy of Science and at the Moscow State University, Moscow, Russia
  35.  A talk “Affine linking numbers, their applications, and operations on generalized strings.” at the Geometry and Topology seminar, Department of Mathematics, University of Pennsylvania, April 8, 2004
  36.  An invited talk “Algebraic structures on generalized strings.” on April 18 2004 at the Special “Homotopical Physics” Section of the Spring Eastern AMS Section Meeting #997, Lawrenceville NJ, held on April 17-18, 2004
  37.  A talk "Affine linking numbers and generalized string homology.” on December 5 2003 at the “Borders in 3-dimensional topology” conference held at the Ohio State University, Columbus, December 5-7, 2003
  38.  A talk "Vassiliev invariants of Legendrian, pseudo-Legendrian, transverse, and framed knots in contact 3-manifolds." at the Geometry and Topology seminar, Mathematics Department, SUNY Buffalo, November 14, 2003
  39.  A talk ``Affine linking numbers, their applications and algebraic structures on generalized strings.” on November 8 2003 at the “Algebraic Topology” Section of the Union College Mathematics Conference, Union College, Schenectady, NY, held on November 8-9, 2003
  40.  A talk “Affine linking and winding numbers and the study of front propagation.” on October 25 2003 at the “Homological Physics” Section of the Fall AMS Southeastern Section Meeting #991, at the University of North Carolina, Chapel Hill, NC, October 24-25, 2003
  41.  A talk “Vassiliev invariant of Legendrian, pseudo-Legendrian and framed knots in contact 3-manifolds.” at the “Gauge Theory and Topology Seminar”, Department of Mathematics, Harvard University, October 10, 2003
  42.  A talk “Vassiliev invariants of Legendrian, pseudo-Legendrian, transverse and framed knots in contact 3-manifolds.” at the Geometric Topology Seminar, Department of Mathematics, Columbia University,  September 19, 2003
  43.  A talk “Affine linking and winding numbers and their applications to the study of causality and of front propagations.” at the “Arnold’s Seminar on Singularity Theory”, Mathematics Department of Moscow State University, Moscow, Russia, September 9, 2003
  44.  A talk "Affine linking numbers and their application to the study of front propagations." at the “Moscow-Petersburg Seminar on Low-Dimensional Mathematics”, Steklov Institute of Mathematics at St Petersburg, Russia, September 5, 2003
  45.  A talk “Algebraic structures on generalized strings and the general theory of affine linking numbers." at the “Rokhlin Topology Seminar”, Steklov Institute of Mathematics at St Petersburg, Russia, September 1, 2003
  46.  A talk “Affine linking and winding numbers and the study of front propagation.” on July 18 2003 at the “XII Oporto meeting in Geometry Topology and Physics”, Universidade do Porto, Portugal, held July 17-20, 2003
  47.  A talk “Affine linking and winding numbers and the study of front propagation.” at the Mathematical Physics Seminar,  Departamento de Matemática Instituto Superior Técnico Lisboa, Portugal, July 17, 2003
  48.  A talk “Affine linking and winding numbers and the study of front propagation.” on July 12 2003 at the “Topological Dynamics and Ergodic Theory” session of the “2003 Summer Conference on Topology and its Applications”, Howard University, held on July 9-12 2003
  49.  A talk “Affine linking and winding numbers and the study of front propagation.” on June 13 2003  at the Lehigh University Geometry and Topology Conference, held on June 12-14, 2003
  50.  A talk "Vassiliev invariants of Legendrian, Pseudo-Legendrian and framed knots in contact 3-manifolds." on June 6 2003 at the “NSF-NSA Conference on Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory and Mathematical Physics”, held at SUNY Potsdam on June 2-June 6, 2003
  51.  A talk "Affine linking numbers and their applications to the study of wave front propagation and causality." on June 4 2003 at the “NSF-NSA conference on Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory and Mathematical Physics”, held at SUNY Potsdam, NY, on June 2-6, 2003
  52.  Colloquium talk "Affine Linking Numbers and the Causality Relation for Wave Fronts." at the Department of Mathematics, Boise State University , Boise, ID, May 13, 2003
  53.  A talk "Vassiliev-Goussarov invariants of Legendrian pseudo-Legendrian and framed knots." at the Topology Seminar, Department of Mathematics, Boise State University, May 12, 2003
  54.  A talk "Affine linking numbers and causality relations for wave fronts." at the Topology Seminar, Mathematics Department, Yale University, March 27, 2003
  55.  A talk “Vassiliev invariants of Legendrian, Pseudo-Legendrian and framed knots in contact 3-manifolds.” at the Topology Seminar, Mathematics Department, Brandeis University, February 12, 2003
  56.  A talk “The universal order one invariant of framed knots in the total spaces of S1 bundles over orientable surfaces F≠ S2, S1 × S1.” on November 10 at the special session on “Invariants of knots and low-dimensional manifolds” of the AMS Southeastrn Section meeting # 982 at Orlando Florida, held on November 9-10, 2002
  57.  An invited talk “Affine linking Numbers and Causality relations for wave fronts.” on November 10 2002 at the special session on “Homotopy Theory and Geometric Topology” at the AMS Southeastrn Section meeting meeting #982 at Orlando Florida, held  on November 9-10, 2002
  58.  A talk "Universal order one Vassiliev invariants of framed knots in the total spaces of S1-bundles over surfaces." at the “Rokhlin Topology Seminar”, Steklov Institute of Mathematics at St. Petersburg, Russia, September 9, 2002
  59.  A talk "The causality relation and affine linking numbers." at the “Rokhlin Topology Seminar”, Steklov Institute of Mathematics at St. Petersburg, Russia, July 8, 2002
  60.  A talk “Framed knots in 3-manifolds and the natural framings of transverse knots.” on March 8 2002 at the “Workshop in Geometric Topology and Geometric Group Theory”, University of Florida, Gainesville held on March 3-10, 2002
  61.  A talk “Vassiliev invariants of Framed, Pseudo-Legendrian and Legendrian knots in contact 3-manifolds.”, on March 4 2002 at the “Workshop in Geometric Topology and Geometric Group Theory”, University of Florida, Gainesville, held on March 3-10, 2002
  62.  A talk “Vassiliev invariants of Framed, Pseudo-Legendrian and Legendrian knots in contact 3-manifolds.” at the Geometry-Topology Seminar, Department of Mathematical Sciences, Binghamton University, Binghampton, NY, February 14 2002
  63.  A talk "Legendrian and Pseudo-Legendrian knots and Vassiliev invariants for them." at the Rokhlin Topology Seminar, St Petersburg Department of Steklov Institute of Mathematics, St Petersburg, Russia, December 17 2001 
  64.  Two talks “Finite order invariants of Legendrian, Transverse and framed knots in contact 3-manifolds, parts I and II.” at the “Rokhlin Topology Seminar”, Steklov Institute of Mathematics at St. Petersburg, Russia, September 3 and 10, 2001
  65.  A talk at the Mathematical Physics seminar at the ETH Zurich, Switzerland 2001
  66.  Invited speaker at the Contact Geometry Workshop at Stanford University, December 13-17 2000
  67.  Talk at the Oberseminar in Complex Geometry, University of Zurich, Zurich, Switzerland, 2000
  68.  Talk at the Topology Seminar at the Max-Planck-Institut fur Mathematik, Bonn,  Germany, 2000
  69.  Colloquium Talk, at the Mathematics Department, University of Siegen, Siegen, Germany, 2000
  70.  Talk at the Geometry Seminar at the Institute of Mathematics of the University of Basel, Switzerland, 2000
  71.  Talk at the Geometry seminar at the Ruhr-Universitat, Bochum, Germany, 2000
  72.  Talk at the Geometry seminar at the Albret-Ludwigs-Universitat, Freiburg, Germany, 2000
  73.  Talk at the Geometry Seminar at the Bonn University, Bonn, Germany, 2000
  74.  Talk at the Geometry and Topology Seminar, University Paul Sabatier, Toulouse, France,2000
  75.  Talk at the Topology seminar, Strasbourg University, Strasbourg, France, 2000
  76.  Talk at the Oberseminar, at the Max-Planck-Institut fur Mathematik, Bonn,  Germany, 1999
  77.  Invited speaker at the "Geometric and symplectic topology" program, Pisa University, Pisa, Italy, 1999
  78.  Talk at the ``Sur les singularites'' seminar at the l'Ecole Normale Superieure in Paris, France, 1999
  79.  Speaker at the “VIII OPORTO Meeting in Geometry Topology and Physics”, Porto, Portugal, 1999
  80.  Two talks at the Symplectic Geometry Seminar at the ETH Zurich, Switzerland, 1998-1999
  81.  Talk at the Geometry Seminar at the Institute  of Mathematics of the University of Basel, Switzerland, 1999
  82.  Talk at the V.I. Arnold's seminar on Singularity Theory, Moscow State University, Russia,1999
  83.  Talk at the Colloquium at the Deptartment of Mathematics at the University of California Riverside, CA, 1997
  84. Talk at the AMS meeting #920 at the University of Maryland, College Park, MD, 1997
  85. Principal speaker at the MSRI workshop ``Combinatorial Problems Arising in Knots and 3-manifolds'', Berkeley, CA, 1997

 

Seminar talks at Dartmouth

1.    “Smooth Cosmic Censorship” at the  Geometry and Topology seminar, Mathematics Department, Dartmouth College,

April 3, 2012

2.      “Conformal maps from spacetimes to the space of Legendrian submanifolds and causality on causally simple spacetimes” at the  Geometry and Topology seminar, Mathematics Department, Dartmouth College, October 11, 2011

3.     “Causal structure on the space of Legendrian spheres isotopic to a sky and some open questions” at the Geometry and Topology seminar, Mathematics Department, Dartmouth College, October 5, 2010

4.     “Legendrian links, causality, and the Low conjecture” at the Geometry and Topology seminar, Mathematics Department, Dartmouth College, April 10, 2009

5.     A sequence of four  talks ``Algebra on Bordism groups of garlands" at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College,  on April 25, May 3, May 17, May 24, 2007.

6.     Two talks “Affine linking number and causality in globally hyperbolic Lorentz manifolds and a roundtrip journey from singular null surfaces to Legendrian mappings, part I.” and “A roundtrip journey from singular null surfaces to Legendrian mappings, part II.”  at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, April 20 and May 18, 2006

7.     Two talks “Applications of Vassiliev invariants to distinguishing pseudo-Legendrian knots, parts I and II.” at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, May 26 and June 2, 2005

8.     A talk “Generalizations of the complex analysis Cauchy integral formula and related algebraic structures on generalized string homology.” at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, March 9, 2004

9.  A talk “Affine linking numbers and their applications to the causality relation.” at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, November 21, 2003

10.   A talk “Universal order one Vassiliev invariants of framed knots in the total spaces of S1-bundles over surfaces.” at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, November 14, 2003

11.  Two talks “Affine winding numbers and their applications to wave propagations, part I” and “Towards the general theory of affine linking numbers part II: Relations with winding numbers and front propagation.” at the Geometry and Topology seminar, Department of Mathematics, Dartmouth College, On February 20 and March 13, 2003

12.   Two talks “Affine linking number and the Causality Relation invariant, parts I       and II.” at the Geometry and Topology seminar, Department of  Mathematics, Dartmouth College on May 14 and 21, 2002

13.   Two talks “Framed knots in 3-manifolds and some new invariants of transverse knots, parts I and II.” at the Geometry and Topology Seminar, Department of Mathematics, Dartmouth College,  October 4 and 11, 2001

 

 

Talks at Undergraduate Conferences

 

1.     A talk “Smooth Structures on Spacetimes” at the XIX Hudson River Undergraduate Mathematics Conference, held at the

Western New England University in Springfield, MA April $21$, $2012$

2.     A talk “Smooth structures on a spacetime.” at the XVIII Hudson River Undergraduate Mathematics Conference, held at the

 Union College, Schenectady NY, April 16, 2011

3.     A talk “Causality and Linking.”at the XVI Hudson River Undergraduate Mathematics Conference, held at the Union College, Schenectady NY, April 18, 2009

4.     A talk “Knot Theory and the Study of Wave Front Propagation.”at the XIII Hudson River Undergraduate Mathematics Conference, Westfield, MA, April 8, 2006

 

Undergraduate Research Supervised

 

1.   Greg Elliot '12, Senior Thesis, Winter-Spring 2012

2.    Yong Su '09, Dartmouth Presidential Scholar student in Fall 2007, Winter 2008.

3.     Evarist Byberi '08, Dartmouth Presidential Scholar student in Fall 2006 and Spring 2007. In 2008 he wrote a senior thesis under my supervision. In Fall 2007 we wrote a joint paper that was published in Commun. Contemp. Math. in 2008.

 

Main Professional Activities

1.     Reviewer for the American Mathematical publication database Mathematical Reviews

2.       Reviewer for the European Mathematical publication database ZentralblattMember

3.       Member  of the ``Mathematics in Moscow Committee'' of the American Mathematical Society, Fall 2007- Spring 2010, Chair of the Committee Fall 2008- Spring 2010 and Fall 2011-Spring 2012