# Home Page

#### Curriculum Vitae Publications

### PERSONAL INFORMATION

Born: 1967, Sverdlovsk, USSR

Citizenship: Russian, Israeli (from 09/2016)

Address: Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel

E-mail: marina.p [] technion.ac.il

web-site: marina-p.info

Interests: global analysis, index theory, elliptic operators, topology, K-theory, mathematical physics, nonstandard analysis

Children: Ira, Inga

### ACADEMIC POSITIONS

10/2023 – now | Visiting Scientist, Department of Mathematics, Technion – Israel Institute of Technology |

10/2020 – 09/2023 | Post-Doctoral Fellow, Department of Mathematics, Technion – Israel Institute of Technology |

**Previous positions in Yekaterinburg, Russia**

2009-2016 | Senior Researcher (part time) at the Ural Federal University |

2008-2016 | Senior Researcher at the Algebra and Topology Department (Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences) |

1994-2008 | Junior Researcher, Researcher, Senior Researcher at the Applied Problems Department (Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences) |

### EDUCATION

10/2016 - 09/2020 | PhD Studies (Pure Mathematics), Department of Mathematics, Technion – Israel Institute of Technology. Supervisor: Prof. Simeon Reich. Thesis: “Spectral Flow and Family Index for Self-Adjoint Elliptic Local Boundary Value Problems on Compact Surfaces” (pdf). |

1997 | PhD degree (Differential Equations), Ural State University. Thesis: "Some Analytic Methods of Investigation of Nonlinear Boundary Problems of Mathematical Physics". |

1990-1994 | PhD Studies (Applied Mathematics): Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences. Supervisor: Prof. Anatoly F. Sidorov. |

1984-1990 | MSc (Summa cum Laude): Department of Mathematics and Mechanics, Ural State University, Sverdlovsk (now Yekaterinburg), USSR. Supervisor: Dr. Valery V. Mansurov. Thesis: “Dendrite Growth in Overcooled Melt”. |

### VISITING POSITIONS

03-05/2016, 10-11/2015 | Einstein Institute of Mathematics, The Hebrew University of Jerusalem (Israel) |

03/2014 | Max Planck Institute for Mathematics (Bonn, Germany) |

05-06/2013, 04-06/2012 | Laboratory of Algebraic Geometry and its Applications, National research university "Higher school of economics" (Moscow, Russia) |

04/2011 | Institute of Molecules and Materials, Radboud University (Nijmegen, Netherlands) |

03-04/2010 | Max Planck Institute for Mathematics (Bonn, Germany) |

10-11/2007 | IHES (Bures-sur-Yvette, France) |

### MSC STUDENT ADVISING

Ural Federal University (Yekaterinburg, Russia):

2010-2011 | Maxim Mornev (currently a SNSF Ambizione postdoc at EPFL, number theory) |

2008-2011 | Daniil Aizenshtein |

### TEACHING

#### MSc courses

2013-2014 | Differential topology (one year course, Ural Federal University) |

2009-2011 | Algebraic geometry (two year course, Ural Federal University) |

#### Mini-courses

International School-Conference for young scientists (Yekaterinburg, Russia):

2016 | Poncelet’s porism and elliptic curves |

2015 | K-theory: topology, analysis, algebra |

The Summer School "Contemporary Mathematics" (Dubna, Russia):

2014 | Nonstandard analysis (video: 1, 2, 3, 4, in Russian) |

2013 | Smooth manifolds and homotopy groups of spheres (video: 1, 2, 3, 4, in Russian) |

2011 | Eight faces of the Poincare homology 3-sphere |

2010 | 3-dimensional manifolds |

### SELECTED PUBLICATIONS

**My papers on Google Scholar** **My papers on arXiv**

- Family index for Fredholm extensions of semi-Fredholm operators.

arXiv:2401.16060 (2024), 37 pp. - From graph to Riesz continuity.

arXiv:2202.03337 (2022), 26 pp. - The continuity properties of discrete-spectrum families of Fredholm operators.

arXiv:2201.09869 (2022), 4 pp. - Spaces of unbounded Fredholm operators. I. Homotopy equivalences.

arXiv:2110.14359 (2021), 24 pp. - Spectral Sections.

Israel Journal of Mathematics 259 (2024), 651–700 (pdf)

arXiv:2008.04672. - Self-adjoint local boundary problems on compact surfaces. II. Family index.

Journal of Noncommutative Geometry, 16 (2022), no. 4, 1213-1257.

arXiv:1809.04353. - Self-adjoint local boundary problems on compact surfaces. I. Spectral flow.

Journal of Geometric Analysis, 31 (2021), no. 2, 1510-1554.

arXiv:1703.06105. - The structure of the category of parabolic equations. I.

CEUR Workshop Proceedings 1662 (2016), 121-133. - The structure of the category of parabolic equations. II.

CEUR Workshop Proceedings 1662 (2016), 134-147. - Factorization of the Reaction-Diffusion Equation, the Wave Equation, and Other Equations.

Proceedings of the Steklov Institute of Mathematics 287 (2014), Suppl. 1, S156-S166.

(text in English, text in Russian) - The spectral flow for Dirac operators on compact planar domains with local boundary conditions.

Communications in Mathematical Physics 322 (2013), no.2, 385-414.

arXiv:1108.0806 - Homeomorphism criteria for the theory of grid generation.

Zh. Vychisl. Mat. i Mat. Fiz. 52 (2012), no.5, 878–882 (in Russian);

arXiv:1504.01087 (in English). - (with M.I. Katsnelson)

Zero-energy states in corrugated bilayer graphene.

Physical Review B 77 (2008), no.20.

arXiv:0802.1409 [cond-mat.mes-hall] - Homeomorphism problems arising in the theory of grid generation.

Proceedings of the Steklov Institute of Mathematics 261 (2008), Suppl.1, S165-S182.

(see also text in Russian). - On the existence of factor sets by external equivalence relations in IST.

Siberian Mathematical Journal 43 (2002), no. 4, 708-713

(see also text in Russian). - External sets properties in IST. The Bulletin of Symbolic Logic 8 (2002), Issue 1, 155-156.
- Heat equation on Riemann manifolds: morphisms and factorization to smaller dimension.

Proceedings of Institute of Mathematics of NAS of Ukraine 43 (2002), 194–200. - On relative near-standardness in IST.

Siberian Mathematical Journal 39 (1998), no. 3, 518-521

(see also text in Russian). - Modeling of solutions of the heat equation and of the Stefan problem with dimension decrease.

Russian Acad. Sci. Docl. Math.**58**(1998), no.1, 88-90. - (with L.D. Zabezhinskii, V.V. Prokhorov, M.N. Mil'shtein, S.G. Stakheev)

Statement and personal-computer-aided realization of the conjugate problem of heat transfer in a power-technological boiler with a moving bed of dispersed heat-transfer agent.

Journal of Engineering Physics and Thermophysics 70 (1997), no. 5, 744–748. - Self-similar solutions of the Stefan problem.

Journal of Engineering Physics and Thermophysics 63 (1992), no. 4, 1032–1036. - The shape of a growing dendrite.

Journal of Engineering Physics and Thermophysics 61 (1991), no. 5, 1394–1400.

## INVITED TALKS

2014 Conference Geometric Structures and Spectral Invariants (Berlin, Germany), invited speaker

## OTHER PROFESSIONAL ACTIVITIES

2012-2016 | International School-Conferences for young scientists (Yekaterinburg, Russia), member of the program committee and chair of the Topology and Geometry section. |

2011 | International School on Algebra and Algebraic Geometry (Yekaterinburg, Russia), organizer |

2011 | International Conference on Algebra and Geometry (Yekaterinburg, Russia), member of the Organizing Committee |

2010, 2011 | Russian School-Conferences for young scientists (Yekaterinburg, Russia), member of the Organizing Committee and of the Program Committee |

2008-2014 | Advisor for the Algebraic Topology learning seminar (Institute of Mathematics and Mechanics, Russian Academy of Sciences / Ural Branch) |

2011-2012 | Advisor for the Category Theory learning seminar (Ural Federal University) |

### AWARDS

2021 | The project proposal “Family Index and Spectral Flow” submitted under the Horizon 2020’s Marie Skłodowska-Curie actions call H2020-MSCA-IF-2020 has been awarded a “Seal of Excellence” by the European Commission (scored 91.4 out of 100) |

2005 | Results were included in the list of the best results of the Ural Branch of Russian Academy of Sciences |

2001 | International Science and Education Development Foundation (ISEDF) Grant "Young scientists of Russia" |

1997-1999 | State Research Grant of Russian Federation for young scientists |

1996 | Results were included in the list of the best results of the Ural Branch of Russian Academy of Sciences |

1996 | The Prize of the Ural Mathematical Society |

1987 | First Prize of the USSR's National Undergraduates Contest in Mathematics |

1987 | First Prize of the Ural Undergraduates Contest in Theoretical Mechanics |

1988 | First Prize of the Regional (Ural, Siberia and Far East) Undergraduates Contest in Computer Sciences |

1983 | First Prize of the USSR's National Junior Contest in Mathematics |

1984 | Second Prize of the USSR's National Junior Contest in Mathematics |