Dr Misha Rudnev

Search results

• 2020

  An Energy Bound in the Affine Group

  Petridis, G., Roche-Newton, O., Rudnev, M. & Warren, A., 3 Jun 2020, In: International Mathematics Research Notices. 0, rnaa130.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access
  6 Citations (Scopus)

• Stronger sum--product inequalities for small sets

  Rudnev, M., Shkredov, I. & Shakan, G., 6 Jan 2020, In: Proceedings of the American Mathematical Society. 148, p. 1467-1479 13 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access
  17 Citations (Scopus)
• 2019

  Bisector energy and pinned distances in positive characteristic

  Murphy, B., Rudnev, M. & Stevens, S. C. C., 2019, (Submitted) In: SUBMITTED.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• New results on sum-product type growth over fields

  Murphy, B., Petridis, G., Roche-Newton, O., Rudnev, M. & Shkredov, I. D., 2 Apr 2019, In: Mathematika. 65, 3, p. 588-642 55 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Product Type 100%
  • Number 66%
  • Characteristics 33%
  • Points 33%
  • Bounds 33%
  39 Citations (Scopus)

• On growth rate in SL_2(F_p), the affine group and sum-product type implications

  Rudnev, M. & Shkredov, I., 2019, (Submitted) In: SUBMITTED. 43 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
• 2018

  Minimising the Sum of Projections of a Finite Set

  Lev, V. F. & Rudnev, M., Sept 2018, In: Discrete and Computational Geometry. 60, 2, p. 493-511 19 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Projection 100%
  • Minimizing 100%
  • Finite Set 100%
  • Graph 20%
  • Order 20%
  1 Citation (Scopus)

  134 Downloads (Pure)

• On discrete values of bilinear forms

  Iosevich, A., Roche-Newton, O. & Rudnev, M., 2018, In: Sbornik: Mathematics. 209, 10, p. 1482--1497

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  3 Citations (Scopus)

• On the number of incidences between points and planes in three dimensions

  Rudnev, M., Feb 2018, In: Combinatorica. 38, 1, p. 219–254 36 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Number 100%
  • Points 100%
  • Bounds 60%
  • Hyperplane 40%
  • Characteristics 20%
  56 Citations (Scopus)

  369 Downloads (Pure)

• On the restriction problem for discrete paraboloid in lower dimension

  Rudnev, M. & Shkredov, I. D., 1 Dec 2018, In: Advances in Mathematics. 339, p. 657-671 15 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Paraboloid 100%
  • Characteristics 50%
  • Dimensional Vector Space 50%
  • Residue Field 50%
  12 Citations (Scopus)

  144 Downloads (Pure)
• 2017

  Elementary methods for incidence problems in finite fields

  Javier, C., Iosevich, A., Lund, B., Roche-Newton, O. & Rudnev, M., 2017, In: Acta Arithmetica. 177, p. 133-142 10 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Circle 100%
  • Finite Field 100%
  • Incidence Problem 100%
  • Elementary Method 100%
  • Points 50%
  6 Citations (Scopus)

  279 Downloads (Pure)

• Group actions and geometric combinatorics in F^d/_q

  Bennett, M., Hart, D., Iosevich, A., Pakianathan, J. & Rudnev, M., Jan 2017, In: Forum Mathematicum. 29, 1, p. 91-110 20 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Classes 100%
  • Points 100%
  • Congruence 100%
  • Finite Field 100%
  • Combinatorics 100%
  32 Citations (Scopus)

  312 Downloads (Pure)

• Growth Estimates in Positive Characteristic via Collisions

  Yazici, E. A., Murphy, B., Rudnev, M. & Shkredov, I., Dec 2017, In: International Mathematics Research Notices. 2017, 23, p. 7148-7189 42 p., rnw206.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Characteristics 100%
  • Points 100%
  • Cardinality 66%
  • Direction 33%
  • Set Point 33%
  24 Citations (Scopus)

  303 Downloads (Pure)

• On distinct cross-ratios and related growth problems

  Rudnev, M., 2017, In: Moscow Journal of Combinatorics and Number Theory,. 7, 3, p. 51--65

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  5 Citations (Scopus)

• On the few products, many sums problem

  Murphy, B., Rudnev, M., Shkredov, I. D. & Shteinikov, Y. N., 1 Dec 2017, (Submitted) In: Journal de théorie des nombres de Bordeaux.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Bounds 100%
  • Subgroup 80%
  • Multiplicative 60%
  • Order 40%
  • Finite Set 20%
• 2016

  New sum-product type estimates over finite fields

  Roche-Newton, O., Rudnev, M. & Shkredov, I. D., 30 Apr 2016, In: Advances in Mathematics. 293, p. 589-605 17 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Number 100%
  • Characteristics 100%
  • Finite Field 100%
  • Product Type 100%
  • Points 50%
  50 Citations (Scopus)

  348 Downloads (Pure)

• On the use of Klein quadric for geometric incidence problems in two dimensions

  Rudnev, M. & Selig, J. M., Jun 2016, In: SIAM Journal on Discrete Mathematics. 30, 2, p. 934-954 21 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Incidence Problem 100%
  • Number 50%
  • Classes 50%
  • Geometry 50%
  • Points 50%
  16 Citations (Scopus)

  492 Downloads (Pure)
• 2015

  Areas of triangles and Beck's theorem in planes over finite fields

  Iosevich, A., Rudnev, M. & Zhai, Y., 1 May 2015, In: Combinatorica. 35, 3, p. 295-308 14 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File
  10 Citations (Scopus)

  258 Downloads (Pure)

• On growth in an abstract plane

  Gill, N., Helfgott, H. A. & Rudnev, M., 20 Dec 2015, In: Proceedings of the American Mathematical Society. 143, p. 3593-3602 10 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File
  3 Citations (Scopus)

  216 Downloads (Pure)

• On the Minkowski distances and products of sum sets

  Roche-Newton, O. & Rudnev, M., 1 Sept 2015, In: Israel Journal of Mathematics. 209, 2, p. 507-526 20 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File
  18 Citations (Scopus)

  297 Downloads (Pure)
• 2014

  Theory of dimension for large discrete sets and applications

  Iosevich, A., Rudnev, M. & Uriarte-Tiero, I., 2014, In: Mathematical Modeling of Natural Phenomena. 9, 5, p. 148--169

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access
  5 Citations (Scopus)
• 2013

  On new sum-product-type estimates

  Konyagin, SV. & Rudnev, M., 2013, In: SIAM Journal on Discrete Mathematics. 27, 2, p. 973–990 18 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Bounds 100%
  • Product Type 100%
  • Constant 50%
  • Combinatorics 50%
  • Complex Plane 50%
  24 Citations (Scopus)

  308 Downloads (Pure)
• 2012

  An improved sum-product inequality in fields of prime order

  Rudnev, M., 2012, In: International Mathematics Research Notices. 2012, 16, p. 3693-3705 13 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Product Sum 100%
  • Prime Order 100%
  • Inequality 100%
  • Cardinality 50%
  • Roots 50%
  27 Citations (Scopus)
• 2011

  An explicit incidence theorem in Fp

  Helfgott, H. A. & Rudnev, M., 2011, In: Mathematika. 57, 1, p. 135--145

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

• Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdős-Falconer distance conjecture

  Hart, D., Iosevich, A., Koh, D. & Rudnev, M., Jun 2011, In: Transactions of the American Mathematical Society. 363, 6, p. 3255 - 3275 21 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Vector space 85%
  • Incidence 60%
  • Unit Sphere 25%
  93 Citations (Scopus)

• On an application of Guth-Katz theorem

  Iosevich, A., Roche-Newton, O. & Rudnev, M., 2011, In: Mathematics Research Letters. 691 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access
  12 Citations (Scopus)
• 2010

  Generalized incidence theorems, homogeneous forms and sum–product estimates in finite fields

  Covert, D., Hart, D., Iosevich, A., Koh, D. & Rudnev, M., Jan 2010, In: European Journal of Combinatorics. 31, issue 1, p. 306 - 319 14 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Finite Field 100%
  • Vector Space 33%
  • Geometry 16%
  • Points 16%
  • Bounds 16%
  20 Citations (Scopus)
• 2009

  Frieman Theorem, Fourier transform, and additive structure of measures

  Iosevich, A. & Rudnev, M., Feb 2009, In: Journal of the Australian Mathematical Society. 86, issue 1, p. 97 - 109 13 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Measures 100%
  • Combinatorics 33%
  5 Citations (Scopus)

• On additive properties of product sets in an arbitrary finite field

  Glibichuk, A. & Rudnev, M., May 2009, In: Journal d'Analyse Mathématique. 108, 1, p. 159 - 170 12 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Finite Field 100%
  • Additive Property 100%
  12 Citations (Scopus)
• 2007

  Distance measures for well-distributed sets

  Iosevich, A. & Rudnev, M., Jul 2007, In: Discrete and Computational Geometry. 38 (1), p. 61 - 80 20 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Integer 100%
  • Measures 100%
  • Classes 100%
  • Points 100%
  • Upper Bound 50%
  12 Citations (Scopus)

• Erdös distance problem in vector spaces over finite fields

  Iosevich, A. & Rudnev, M., Dec 2007, In: Transactions of the American Mathematical Society. 359 (12), p. 6127 - 6142 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  122 Citations (Scopus)

• Lax pairs for higher-dimensional evolution PDEs and a 3+1 dimensional integrable generalization of the Burgers equation

  Rudnev, M., Yurov, AV. & Yurov, VA., 2007, In: Proceedings of the American Mathematical Society. 135, 3, p. 731 - 741

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Generalisation 100%
  • PDE 100%
  • Lax Pair 100%
  • Burger Equation 100%
  • Symmetry 66%
  1 Citation (Scopus)

• On the Mattila integral associated with sign indefinite measures

  Iosevich, A. & Rudnev, M., Apr 2007, In: Journal of Fourier Analysis and Applications. 13 (2), p. 167 - 173 7 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  4 Citations (Scopus)
• 2006

  A model for separatrix splitting near multiple resonances

  Rudnev, M. & Ten, VV., Jan 2006, In: Regular and Chaotic Dynamics. 11 (1), p. 83 - 102 20 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Model 100%
  • Splitting 100%
  • Hamiltonian Systems 66%
  • Estimates 33%
  • Bifurcation 33%
  2 Citations (Scopus)

• An inverse problem of Hamiltonian dynamics

  Rudnev, M. & Ten, VV., 2006, In: Proceedings of the American Mathematical Society. 134 (11), p. 3295 - 3299

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Hamiltonian Systems 100%
  • Manifold 100%
  • Hamiltonian Dynamic 100%

• Combinatorial complexity of convex sequences

  Iosevich, A., Konyagin, S., Rudnev, M. & Ten, VV., Jan 2006, In: Discrete and Computational Geometry. 35 (1), p. 143 - 158 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Complexity 100%
  • Incidence 100%
  • Show 50%
  • Motivation 50%
  • Assumption 50%
  19 Citations (Scopus)

• Integrability versus topology of configuration manifolds and domains of possible motions

  Rudnev, M. & Ten, VV., Jan 2006, In: Archiv der Mathematik. 86 (1), p. 90 - 96

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Configuration Manifold 100%
  • Topology 100%
  • Domains 100%
  • Torus 33%
  • Sufficient Condition 33%
  1 Citation (Scopus)
• 2005

  Non-isotropic distance measures for lattice-generated sets

  Iosevich, A. & Rudnev, M., 2005, In: Publicacions Matematiques. 49 (1), p. 225 - 247

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Measures 100%
  • Lattices 100%
  • Upper Bound 33%
  • Convex Body 33%
  3 Citations (Scopus)
• 2004

  Sharp upper bounds for splitting of separatrices near a simple resonance

  Rudnev, M. & Ten, VV., 2004, In: Regular and Chaotic Dynamics. 9 (3), p. 299 - 336

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Parameters 100%
  • Upper Bound 100%
  • Measures 50%
  • Characteristics 50%
  • Torus 50%
  2 Citations (Scopus)
• 2003

  A combinatorial approach to orthogonal exponentials

  Iosevich, A. & Rudnev, M., Jan 2003, In: International Mathematics Research Notices. 50, p. 2671 - 2685 15 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  13 Citations (Scopus)

• Darboux transformation for classical acoustic spectral problem

  Yurova, A., Yurov, A. & Rudnev, M., 2003, In: International Journal of Mathematics and Mathematical Sciences. 49, p. 3123 - 3142

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Acoustics 100%
  • PDE 50%
  • Utilization 25%
  • Dimensions 25%
  • Dielectrics 25%
  4 Citations (Scopus)
• 2000

  Erratum to Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems

  Rudnev, M. & Wiggins, SR., 2000, In: Physica D: Nonlinear Phenomena. 145(3-4), p. 349 - 354

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• On a homoclinic splitting problem

  Rudnev, M. & Wiggins, S. R., 2000, In: Regular and Chaotic Dynamics. 5, 2, p. 227-242 16 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Torus 100%
  • Submanifold 100%
  • Vector Field 50%
  • Flow 50%
  • Unstable Manifold 50%
  9 Citations (Scopus)
• 1999

  On a partially hyperbolic KAM theorem

  Rudnev, M. & Wiggins, S. R., 1999, In: Regular and Chaotic Dynamics. 4, 4, p. 39--58

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
  3 Citations (Scopus)
• 1998

  Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems

  Rudnev, M. & Wiggins, SR., 1998, In: Physica D: Nonlinear Phenomena. 114(1-2), p. 3 - 80

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  21 Citations (Scopus)
• 1997

  KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems

  Rudnev, M. & Wiggins, SR., 1997, In: Journal of Nonlinear Sciences and Applications. 7(2), p. 177 - 209

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  23 Citations (Scopus)