Dr. Anna Gusakova
Research Interests
- Random polytopes, random tessellations, random graphs
- Limit theorems for high-dimensional structures
- Stochastic and convex geometry
- Zeroes of random polynomials, point processes
- Number theory
Short CV
- Since April 2019: PostDoc in RTG 2131 at Ruhr University Bochum
- Jan. 2017 - Dec. 2018: Ph.D. student in IRTG 2235 at Bielefeld University (Supervisor: Prof. Dr. Friedrich Götze)
- Sep. 2015 - Dec. 2016: Ph.D. student in Institute of Mathematics of National Academy of Sciences of the Republic of Belarus (Supervisor: Prof. Dr. Vasili Bernik)
- Sep. 2014 - Jun. 2015: Master of Science in Mathematics - Researchers Training Institute of National Academy of Sciences of the Republic of Belarus (Supervisor: Prof. Dr. Vasili Bernik)
- Sep. 2013 - Aug. 2015: Junior Researcher at Institute of Mathematics of National Academy of Sciences of the Republic of Belarus (Department of Number Theory)
- Sep. 2009 - Jun. 2014: Bachelor of Science in Security Engineering and Mathematics - Belarusian State University
Publications
-
The β-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions (joint work with Christoph Thäle and Zakhar Kabluchko)
Preprint: arXiv:2104.07348 -
The β-Delaunay tessellation II: The Gaussian limit tessellation (joint work with Christoph Thäle and Zakhar Kabluchko)
Preprint: arXiv:2101.11316 -
The β-Delaunay tessellation I: Description of the model and geometry of typical cells (joint work with Christoph Thäle and Zakhar Kabluchko)
Preprint: arXiv:2005.13875 -
Concentration on Poisson spaces via modified Φ-Sobolev inequalities (joint work with Christoph Thäle and Holger Sambale)
Stochastic Processes and their Applications (2021+) -
Sharp inequalities for the mean distance of random points in convex bodies (joint work with Gilles Bonnet, Christoph Thäle and Dmitry Zaporozhets)
Advances in Mathematics 386, article 107813 (2021), 27 pages -
On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems (joint work with Christoph Thäle)
Mathematika, volume 67, no. 2 (2021), pp. 434-446 -
The volume of simplices in high-dimensional Poisson-Delaunay tessellations (joint work with
Christoph Thäle)
Annales Henri Lebesgue, volume 4 (2021) , pp. 121-153. -
Concentration inequalities for functionals of Poisson cylinder processes (joint work with Anastas Baci, Carina Betken and
Christoph Thäle)
Electronic Journal of Probability, Article 128 (2020), 27 pages. -
On the distribution of Salem numbers (joint work with
Friedrich Götze)
Journal of Number Theory, volume 216 (2020), pp. 192-215. -
Distribution of complex algebraic numbers on the unit circle (joint work with
Friedrich Götze, Zakhar Kabluchko and Dmitry Zaporozhets)
Journal of Mathematical Sciences, volume 251 (2020), pp. 54–66. -
Random affine simplexes (joint work with
Friedrich Götze and Dmitry Zaporozhets)
Journal of Applied Probability, volume 56, no. 1 (2019), pp. 39-51. -
On algebraic integers in short intervals and near smooth curves (joint work with Friedrich Götze)
Acta Arithmetica, volume 179, no. 3 (2017), pp. 251 - 265. -
Upper and lower bounds for the number of algebraic points on short intervals (joint work with Vasili Bernik and Alexey Kudin)
Chebyshevskii Sb., volume 18, no. 4 (2017), pp. 115 - 126 (Russian). -
On distribution of points with conjugate algebraic integer coordinates close to planar curves (joint work with Vasili Bernik and Friedrich Götze)
Anal. Probab. Methods Number Theory (2017), pp. 11 - 23 . -
On points with algebraically conjugate coordinates in neighbourhood of smooth curves (joint work with Vasili Bernik and Friedrich Götze)
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. 448 (2016), pp. 14 - 47.
Translation in Journal of Math. Sci., volume 224, no. 2 (2017), pp. 176 - 198. -
On points with algebraically conjugate coordinates close to smooth curves (joint work with Vasili Bernik and Friedrich Götze)
Moscow Journal of Combinatorics and Number Theory, volume 6, no. 2 - 3 (2016), pp. 57 - 100. -
Distribution of special algebraic points in domains of small measure
Chebyshevskii Sb., volume 17, no. 1 (2016), pp. 50 - 69 (Russian) . -
Distribution of algebraic points in domains of
small measure and near the surfaces (joint work with Vasili Bernik and Alexey Ustinov)
Chebyshevskii Sb., volume 16, no. 3 (2015), pp. 78 - 94 (Russian) .
-
Application of Probability Methods in Number Theory and Integral Geometry
Ph.D. thesis (advisor Prof. Dr. Friedrich Götze)
Selected talks
-
Random simplicial tessellations: high-dimensional probabilistic behaviour of the typical cells
Probability & Statistics Seminar, Luxembourg University, 20 May, 2021 -
Limiting theorems for Poisson-Delaunay tessellation
Asymptotic Geometric Analysis, July 1 - 6, 2019, Euler International Mathematical Institute, Saint-Petersburg, Russia -
Concentration inequalities for functionals of Poisson cylinder processes
Conference "Stochastic Geometry", September 16 - 20, 2019, Euler International Mathematical Institute, Saint-Petersburg, Russia -
Distribution of algebraic numbers and their connection to the roots of random polynomials
Seventh Bielefeld-SNU Joint Workshop in Mathematics, February 26 - March 1, 2019, Center for Interdisciplinary Research, Bielefeld. -
Counting complex algebraic numbers on the unit circle.
International Conference on Number Theory, September 9 - 15, 2018, Palanga, Lithuania. -
Random affine simplexes.
Probability Seminar, April 3, 2018, KAIST, Daejeon, South Korea. -
Distribution of complex algebraic numbers on the unit circle.
The third Indo-Russian meeting in probability and statistics, January 8 - 12, 2018, Indian Institute of Science, Bangalore, India. -
Random affine simplexes.
Seminar on Probability Theory and Mathematical Statistics, November 24, 2017, PDMI, St. Petersburg, Russia. -
Integral geometry formulas for ellipsoids.
Stochastic Geometry Seminar, July 27, 2017, KIT, Karlsruhe, Germany. -
On the distribution of points with conjugate algebraic coordinates near smooth curves.
Workshop on Diophantine approximation and related fields, June 26 - 30, 2017, University of York, York, England. -
Davenport’s problem: an overview.
Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics, October 9 - 14, 2016, Mathematisches Forschungsinstitut, Oberwolfach, Germany. -
On algebraic integers in short intervals and near the smooth curves.
Yu.V.Linnik Centennial Conference: Analytical methods in number theory, probability theory and mathematical statistics. September 14 - 18 , 2015, Euler International Mathematical Institute, St. Petersburg, Russia.
Teaching
Summer term 2021
Exercise classes in "Complex Analysis I"
Winter term 2020/2021
Exercise classes in "Mathematik für Biologen"
Summer term 2020
Seminar on Probabilistic number theory (jointly with Christoph Thäle)
Winter term 2019/2020
Seminar on Measure theory (jointly with Christoph Thäle)
block seminar
Research visits
- March - August, 2018: Visiting Student Researcher in Korea Advanced Institute of Science and Technology, Daejeon, South Korea (advisor: Ji-Oon Lee)
- Visiting Researcher of CRC 701 (Bielefeld University), see visits .
Address
Dr. Anna Gusakova
Faculty of Mathematics
Ruhr University Bochum
Room IB 2/121
44780 Bochum
Germany
Phone: 0234 - 32 - 28988
Email: anna.gusakova@rub.de