Dmitri Burago
Education: Ph.D., St. Petersburg State University, 1992
CV, 2024
Dmitri Burago
Address: Department of Mathematics
PennState University
McAllister Building State College PA 16802
Phone : 1-814-441-7520
Email: burago@math.psu.edu
skype: dburago
Selected Awards and Achievements
The Best Young (below 30) Mathematician Award of St.-Petersburg
Mathematical Society (1992)
Faculty Scholar Medal for Outstanding Achievements, The Penn-
sylvania State University (1995)
Invited to the European Congress of Mathematicians, (1996)
Alfred P. Sloan Research fellowship (1997 -2001).
A 45-minute Invited Address at the International Congress of
Mathematicians (1998)
The Leroy P. Steel Prize for Mathematical Exposition by the American
Mathematical Society (AMS) for 2014
Non-interrupted NSF support with summer research salary (1995-
2020. Did not apply in 2020.)
Named Distinguished Professor of Mathematics (2012).
A book \A Course in Metric Geometry", 415 pages, co-authored with
Yu. Burago and S. Ivanov, is published by the AMS (2001) and it has
been awarded the Steel Prize in 2014.
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Scienti c Degrees
Candidate of Physical and Mathematical Sciences
(corresponds to Ph.D.), St.-Petersburg State University, 1992.
Diploma of Mathematician Summa Cum Laude
(corresponds to M.S.) St.-Petersburg State University, 1986.
Employment
2000 { present Professor ( Now Distinguished Professor)
(Associate Head for Graduate Studies 2003-2007)
Department of Mathematics
Pennsylvania State University
1998 { 2000 Associate Professor
Department of Mathematics
Pennsylvania State University
1995 { 1998 Assistant Professor
Department of Mathematics
Pennsylvania State University
1994 { 1995 Post Doc as Lecturer
Department of Mathematics
David Rittenhouse Laboratory
University of Pennsylvania
1986 { 1994 Scienti c Researcher
Laboratory for Theory of Algorithms,
St.-Petersburg Institute for Informatics and Automation
Russian Academy of Sciences.
1990 { 1994 Assistant Professor
Department of Mathematics and Mechanics,
St.-Petersburg State University, Russia
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Previous Research Grants
NSF Grant Geometry, Dynamics, and PDEs in Riemannian and Finsler
Spaces
September 15, 2015 to August 31, 2020.
Sole Principal Investigator.
Total: $350,964
NSF Grant DMS{1205597
Sole Principal Investigator.
Dates: September 1, 2012 to August 31, 2015. Total budget: $145,000.
NSF Grant DMS-0905838 Sole Principal Investigator. Dates: Septem-
ber 1, 2009 to August 31, 2012. Total budget: $138,537.
NSF continuing Grant DMS-0412166, A01 for July 15, 2004 to June
30, 2009 with 2 months of summer research salary per year.
NSF Conference grant with S. Katok, Ya. Pesin, for falls 2006 { 2008.
NSF Grant DMS-0604113 (change of PI) for July 1, 2008 to June 30, 2009.
NSF continuing Grant DMS-0103739 for June 15, 2001 to May 31, 2004
with 1.6 months summer research salary per year.
CRDF Joint Research Grant for 2001-2004.
Co-Investigators:
S. Alexander, R. Bishop, Yu. Burago, S. Buyalo, S. Ivanov, V. Kobelski
Sloan Research Fellowship
September 1997 - September 2001. Co-investigators: none.
NSF Grant DMS-9803129 granted for June 1, 1998 to May 31, 2001.
with 2 months summer research salary per year. Co-investigators: none.
NSF Grant DMS 95-05175 granted for June 1995 - May 1998.
with 2 months summer research salary per year. Co-investigators: B. Kleiner,
C. Croke, D. DeTurk.
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CRDF Joint Research Grant for 1996-1997. Co-Investigators:S. Alexan-
der, R. Bishop, Yu. Burago, S. Buyalo, S. Ivanov, V. Kobelski
Fellowship of \Deutsche Forschungsgemeinschaf" (DFG)
Dates: 11/15/93 { 2/15/94.
School Outreach Program
Participation on the Departmental VIGRE grant, in charge of the School
Outreach Section (the program is designed to organize and teach optional
mathematical classes at State College schools) 1999-2004.
Mentoring several undergraduate students.
Running the departmental weekly Geometry Luncheon Seminar.
Committees
Departmental Colloquia and Distinguished Lectures Committee, since 2018.
University Graduate Council, 2015 - 2016.
University Promotion and Tenure Committee, 2015 - 2016.
University Joint Curriculum Committee, 2015 - 2016.
Departmental Personnel Committee, 2015 - 2017.
Departmental Colloquia and Distinguished Lecture Committee, 2015 - present.
Departmental PT Committee, 2002-2013. Chair since 2006. Also fall 2017
- spring 2018.
Departmental Policy Committee, member, 1998-2002.
Departmental Executive Committee, 2003-2006.
Graduate Committee, 2003-2007; Chair (member after July 2006).
Undergraduate Committee, 2003-2007.
GTA Oversight Committee, 2003 - 2006.
Personnel Committee, 2003 - 2006.
Numerous Ph.D, Comprehensive, and Qualifying Exams Committees.
Currently serving on Departmental Colloquia and Special Lectures Com-
mittee.
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Membership and Professional Organizations:
A member of the Rokhlin Prize panel, since 2010 - July 2019.
Editorial board, ERA-AMS (now AIMS), since 1998 until it seased to exist
in2020.
Editorial Board, Journal of Topology and Analysis, since 2007.
Editorial Board, Geometry and Topology, since 2008.
Member of St.Petersburg Mathematical Society, since 1992.
Member of Math/Computer Sci CDRF Grant Panel, 1996, and a number of
NSF Panels.
Reviewing papers for GAFA, Research Letters, Erg.Th & Dyn. Syst,
Matemateschen Annalen, Annals of Mathematics, Journal of Di . Ge-
ometry, Africa Matematica, Acta Mathematics, International Journal of
Mathematics, Duke Math. Journal, J. Di . Geom, Communications Math.
Physics, Michigan Math. Journal, Israeli Math. Journal, Nonlinearity, J.
Di . Geometry, J. fur die reine and angewandte Mathematik, Annals of
Geometric Analysis, Proc. AMS, Proc. IHES and many others.
Reviewing NSF, ISF, GIF, CRDF, US-Israeli BSF proposals.
5
Conferences Organized and Co-Organized:
Special Session at the Lowell Meeting of the AMS, April 2000.
Geometry Day of the PennState-Maryland Workshop, 2005, 2007, 2008.
Conference on Metric and Alexandrov Geometry, Guangzhou, Nov. 2007.
Conference on Metric Geometry, Beijing, Nov. 2008.
Teaching Experience 26 of teaching in the US. All kind of courses:
undergraduate, graduate numbered, and special topics. Several month-long
courses in Europe and China. Vast teaching experience in Russia before
relocating to the US 26 years ago. Extremely large experience in teaching
talented schoolchildren, both in Russia and the USA.
Students
S. Ivanov, Ph. D, 1995, St. Petersburg State University.
S. Ferleger, Ph. D, 1998, Penn State University.
H. Lim, MS, 1997, Penn State University.
A. Viro, MS,1999, Penn State University.
E. Johnson, MS, 1999, Penn State University.
S. Krat, Ph. D, 2005, Penn State University.
D. Schoenthal, Ph. D, 2006, Penn State University.
N. Zinoviev, MS, 2006, Penn State University.
W.K. Ho, Ph. D, 2009, Penn State University.
S. Orshansky, Ph. D, 2010 Penn State University.
Dong Chen, Ph.D. 2017 Penn State University.
Jingpeng Lu, Ph. D, 2019 Penn State University.
David Huges, Ph. D, 2019 Penn State University.
Chris Fadden, MS, 2019, Penn State University.
Hongda Qui, Ph.D, current, Penn State University.
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Undergraduate Advising
Advising undergraduate students from option: System Analysis, 1997 {
2003.
Boris Kris, PSU, 2017.
Advising Zhiyu Zhao 2017-2018, continued working with her after she grad-
uated.
Advising for Schreyer College of Honor, 2023-now.
Invited Conference and Seminar Talks, Colloquia [Speaker].
1. \Surfaces with Finite Curvature", St.-Petersburg State University,
Russia (1983)'
2. \Computation of Entropy", St.-Petersburg State University, Russia
(1984).
3. \Unboundedness of Horns in Euclidean Space", Steklov Institute for
Mathematics, St.-Petersburg, Russia (1984).
4. \Almost Flat Surfaces", Steklov Institute for Mathematics, St.-Petersburg,
Russia (1984).
5. \Flows with Positive Entropy", Steklov Institute for Mathematics,
St.-Petersburg, Russia (1986).
6. \Entropy and Non-Invariant Partition", Moscow State University,
Russia (1987).
7. \The Solution of Split-Find Problem", Steklov Institute for Mathe-
matics, St.-Petersburg, Russia (1990).
8. \Limit Norms", Steklov Institute for Mathematics, St.-Petersburg,
Russia (1990)'
9. \Metric Entropy of Some Geometric Systems", Meeting on Hyper-
bolic Behavior of Dynamical Systems, Paris, (1990).
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10. \Quasi-Periodic Metrics", Steklov Institute for Mathematics, St.-
Petersburg, Russia (1991).
11. \Geodesics of Periodic Metrics" International Conference on Dy-
namical Systems, St.-Petersburg (1991).
12. \Geodesics of Periodic Metrics", University of Milano, Italy (1992)
13. \Riemannian Geometry and Mechanics", University of Milano, Italy
(1992).
14. \Periodic Metrics and Finsler Geometry" International Conference
on Geometry and Global Analysis, Munster (1992).
15. \Limit Norm" Lobachevsky semester, St.-Petersburg, Russia (1992).
16. \Embeddings of Finsler Manifolds", Mathematical Institute of Flo-
rence, Italy (1992).
17. \Finsler Submanifolds", Steklov Institute for Mathematics, St.-
Petersburg, Russia (1993).
18. \Asymptotic Properties of Periodic Metrics", Ecole Polytechnique,
France (1993).
19. \Split- nd Problem", University of Poitiers, France (1993).
20. \Complexity and Dynamics", University of Poitiers, France (1993).
21. \Finsler Submanifolds", University of Lion, France (1993).
22. \Complexity of Splitting and Merging of Linear Data", University
Paris-Sud, France (1993).
23. \Computational Complexity and Dynamical Systems", A series of 4
lectures, ENSTA, Paris (1993).
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24. \Hopf's Conjecture", Ecole Polytechnique, France (1994).
25. \Tori without Conjugate Points", University of Lion, France (1994).
26. \E. Hopf Conjecture", Princeton University, USA (1994).
27. \Tori Without Conjugate Points", ETH, Zurich (1994).
28. \Complexity of Strategies" Workshop on Algorithmic Complexity of
algebraic and geometric Models, Paris (1994).
29. \E. Hopf's Conjecture" Workshop on Dynamical Systems and Re-
lated Topics, Penn State University (1994).
30. \Solution of Hopf's Conjecture" IHES, France (1994).
31. \Asymptotic Volume Growth", Stony Brook University (1994).
32. \Asymptotic Geometry of Tori", Penn State University (1994).
33. \E. Hopf's Conjecture", Colloquium, Michigan State University,
(1994).
34. \Integral Geometry in the Proof of Hopf Conjecture", Michigan
State University (1994).
35. \Embeddings of Finsler Metrics", University of Frieburg, Germany
(1994).
36. \Unboundness of Complete Surfaces with Finite Integral Curvature",
University of Frieburg, Germany (1994).
37. \Geodesics on Tori", University of Frieburg, Germany (1994).
38. \Solution of the Hopf Conjecture", Colloquium, University of Frieburg,
Germany (1994).
39. \Hopf's Conjecture", Steklov Institute for Mathematics, St.-Petersburg
(1995).
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40. \Finsler Manifolds, Families of Convex Bodies and Periodic Met-
rics", Colloquium, Penn State University (1995).
41. \Shapes of Balls of Limit Norms", A series of 2 lectures, Penn State
University (1995).
41. \Geometry of Periodic Metrics" A series of 3 lectures, Penn State
University (1995).
43. \Volume Growth in Periodic Metrics", University of California, Los
Angeles (1995).
44. \E. Hopf's Conjecture" Conference on Geometric Analysis, Irvine
(1995).
45. \Asymptotic Geometry of Tori", Geometry Festival, Stony Brook
(1995).
46. \Asymptotic Invariants of Periodic Metrics", Topology Festival, Cor-
nell University (1995).
47. \Tori without Conjugate Points", Yale University (1995).
48. \Collisions of Hard Balls and Singular Geometry", Penn State Uni-
versity (1996).
49. \Asymptotic Isoperimetric Constant", Steklov Institute for Mathe-
matics, St.-Petersburg (1996).
50. \Singularities of Limit Norm", Steklov Institute for Mathematics,
St.-Petersburg (1996).
51. \Geometry of Billiard Systems", School on Dynamical Systems with
Singularities, Vienna (1996).
52. Colloquium, Penn State University, (1996).
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53. \Dispersing Billiards and Alexandrov Spaces Curvature Bounded
Above", Maryland State University (1996).
54. \Collisions of Hard Balls and Singular Spaces of Non-positive Cur-
vature", University of Pennsylvania (1996).
55. Colloquium, Michigan State University (1996).
56. Colloquium, MIT (1996).
57. Seminar Talk, \On the geometry of tori", Stanford University (1996).
58. \Separated nets and Jacobians of Lipshitz homeomorphisms", Uni-
versity of Illinois at Urbana-Champaign (1997).
59. Colloquium, Steklov Institute for Mathematics (1997).
59. Seminar talk, \Singularities of the stable norm of tori", Conference
on Variational Methods in Mechanics, Princeton (1997).
60. \Semi-dispersing billiards and non-positively curved spaces", Con-
ference on De erentialgeometrie im Grossen, Oberwolfach (1997).
61. Colloquium, University of Toronto, Canada (1998).
62. IPST at University of Maryland, a series of two lectures (1998).
63. A series of three lectures, Strasbourg University, France (1998).
64. \Minimal surfaces in Banach spaces", University of Freiburg, Ger-
many (1998).
65. \Jacobians of Lipschits Homeomorphisms", University of Berne,
Switzerland (1998).
66. Wasatch Conference: A series of two invited lectures, University of
Utah (1998).
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67. \Hard ball gas and Alexandrov spaces of curvature bounded above",
International Congress of Mathematics (1998) [45-minute invited lecture].
68. \On the relationship between quasi-isometries and bi-Lipschits equiv-
alence", Conference on Rigidity, Paris (1998).
69. \Separated nets in the palne", Moscow State University (1999).
70. Colloquium, Tufts University (1999).
71. Colloquium, University of Basel, Switzerland (1999).
72. IMA 1999 Summer Program for Graduate Students, a week-long
section on \Geometric Control Theory" (1999).
73. \Geometry of tori: open problems", AMS Summer Research Insti-
tute in Ergodic Theory, Plenary Lecture (1999).
74. \Bi-Lipschits equivalence and quasi-isometries", Maryland State
University (1999).
75. \Minimal surfaces in normed spaces, symplectic lling volume and
asymptotic geometry of tori", ETH, Zurich (1999).
76. \Minimal surfaces in normed spaces, symplectic lling volume and
asymptotic geometry of tori "University of Chicago (1999).
77. \Besicovitch-type inequalities in Finsler geometry", University of
Michigan (1999)
78. \On the asymptotic volume of Finsler tori", University of Pennsyl-
vania (1999).
80 \Asymptotic volume of Finsler tori and Minimal surfaces in normed
spaces", Princeton University, (1999)
81. \Bi-Lipschits equivalence of separated nets and Jacobians of Lips-
chits homeomorphisms", Princeton University, (1999).
12
82. \Counting collisions of hard balls using non-positively curved spaces",
student-faculty colloquium, Maryland State University, (1999).
83. EuroConference on Ergodic theory, geometry and Rigidity. Cam-
bridge, 2000.
84. Summer school on PDE, Edinburgh, Scotland: a series of 6 lectures
(2000).
85. SUNY Stony Brook, (2000).
86. University of Michigan, colloquium, (2000).
87. Colloquium, Tel Aviv University, (2000).
69. Universite de Louvain (Belgium), a series of 3 lectures, (2000)
70. Newton Institute, Cambridge, UK, (2000).
71. Colloquium, Michigan State University, (2001).
Seminar lecture, Michigan State University, (2001).
22. \Geometry of Periodic Media", ARKANSAS SPRING LECTURE
Series 2001.
23. \Gaussian measures of surfaces", IMA summer conference on inverse
problems, Minneapolis, 2001.
24. \Two scales in sequential dynamics and geometric properties of con-
jugacy classes", confrerence: Logic and Complexity in Computer Science,
Paris, 2001.
72.\Geometry of conjugacy classes", Steklov Institute, (2001).
73. A series of 3 lectures, University of Washington, Seattle, (2002).
74. A series of 3 lectures, University of Maryland (2002).
13
75. \Rectifying Penrose lattices", Steklov Institute, Russia, (2002).
76. \Counting collisions using Alexandrov spaces", University of Oulu,
Finland, 2002.
77. \On Gaussian Measures of Surfaces", International Conference ded-
icated to the memory of A.D. Alexandrov, St. Petersburg, 2002.
78. \On Partially Hyperbolic Automorphisms of 3-Manifolds", Con-
ference \Arnold's Di usion" dedicated to the 60th birthday of J. Mather,
Princeton, 2002.
79. \Jacobians of Lipschitz homeomorphisms", University of Helsinki,
Finland, (2002).
80. A series of 2 lectures, Tel Aviv University, Israel, (2002).
81. Seminar lecture, University of Toronto, 3 lectures,(2002)
82. \On Partially Hyperbolic Automorphism of 3-Manifolds", ETH
Zurich, (2003)
83. \Partially Hyperbolic Systems on 3-Manifold with Abelian Funda-
mental Group", \Kolmogorov's Congress, an Invited Lecture, Moscow, 2003.
84. \Unbounded Bi-Invariant Quasi-Semi Norms on Large Groups", Ari-
zona State University, 2003.
85. \Distance-Volume Estimates", University of Washington, 2003.
82. "Unbounded semi-norms", University of Washington, 2004.
86. \Unbounded bi-invariant quasi-norm on groups of geometric origin.",
international conference.
87. Conference Representation Theory, Dynamical Systems, and Asymp-
totic Combinatorics, St. Petersburg, Russia, 2004.
88. \On the \Minimality of Flats" Problem of Busemann and a Gen-
eralization of the Classic Existence Theorem of Minkowski", Colloquium,
14
University of Northern Florida at Gainesville, 2003.
89. \Volume Estimates via Boundary Distance Function, a problem
of Busemann, and a Generalized Minkowski Existence Theorem." Interna-
tional conference: Perspectives in Inverse Problems, Helsinki, Finland, 2004.
90. \Convexity vs Ellipticity for General Surface Are Functionals", Uni-
versity of Michigan, 2004.
91. \Unbounded Quasi-Semi-Norms on Groups", Steklov Institute, Moscow,
2004.
92. \Boundary Rigidity of Almost Flat Metrics", University of Wash-
ington, 2004.
93.\Boundary Rigidity and Minimality of Metrics Close to Flat Ones",
University of Pennsylvania, 2005.
94. \Boundary Rigidity of Metrics Close to a Flat One", one-day special
international sessions Representation Theory, Geometry, and Related Top-
ics, Steklov Institute, 2005.
95. A series of two talks, International Conference on Finsler Geometry,
Lumini, France, 2005.
96. \Area Spaces: First Steps", Steklov Institute for Math, 2005.
97.Blumental Lecture Series at Tel Aviv University, Israel, 2005.
98. \How to choose good coordinates?", University of Washington, 2006.
99. \On Boundary Rigidity", Yale University, 2006.
100. \Handling Branching Foliations", University of Pennsylvania, 2006.
32. \On the existence of quasi-norms on some groups of geometric ori-
gin", Oberwolfach, Germany, 2006.
15
93. \Partially Hyperbolic Di eos of 3-manifolds", University of Wash-
ington, 2006.
94. "Handling Branching Foliatons", Steklov Institute, St. Petersburg,
2006.
95. Colloquium, Moscow Independent University, 2006.
96. "Boundary Rigidity of nearly at metrics", Fudan University, 2006.
97. Colloquium, UHK, Hong Kong, 2006.
98. Colloquium, San Yat Sen University, 2006.
99. Colloquium, Peking University, 2006.
100. \Partially hyperbolic di eomorphisms and branching foliations",
Chinese Academy of Science, Peking, 2006.
101. 13 Graduate Recruitment talks in China, Canada, Russia, USA,
2006.
102. \Inverse problems: Geometric Approach", University of Helsinki,
Finland, 2007.
103. \Invariant norms on Groups", Russian{German International Con-
ference, St. Petersburg, Russia, 2007.
104. \Partially Hyperbolic Di eomorphisms of 3-Manifolds", Conference
on Dynamical Systems, Lisbon, Portugal, 2007.
105. \From Asymptotic geometry of Tori to Boundary Rigidity", Cur-
vature and Shape, Muenster, Germany, 2007.
106. \Boundary Rigidity and Volume Minimality", Metric and Alexan-
drov Geometry", Guangzhou, China, 2007.
107. \Area Spaces", University of Washington, Seattle, 2007.
108. \Area Spaces", Steklov Institute, St. Petersburg, Russia, 2007.
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109. Colloquium, Peking University, Beijing, China, 2007.
110. Colloquium, Rutgers University, 2008.
111. \Boundary rigidity: a geometric approach", University of Wash-
ington, 2008.
122. \Boundary rigidity of metrics closed to at ones", Glimpses in Ge-
ometry, Lyon, France, 2008.
113. \Dynamical Coherence of Partially Hyperbolic Di eomorphisms on
T3", "Brinfest", University of Maryland, 2008.
114. \Area Spaces: First Steps", Geometric group theory, hyperbolic dy-
namics and symplectic geometry, Oberwolfagh, Germany, 2008.
115. \On some unsolved problems in Geometry", Geometry Seminar,
Steklov Institute, 2008.
116. \Some open problems in Geometric Group Theory, Riemannian
and Finsler Geometry", Colloquium, Steklov Institute, 2009.
117. "Minimal surfaces in Normed Spaces", Conference on Finsler and
Minkowski geometry, Fribourg, Switzerland, 2009.
118. \On topological aspects of the Dvoretzky Theorem", University of
Washington, 2009.
119. A series of three lectures, Duke University, 2009.
120. \From Asymptotic Volume of Tori to Boundary Rigidity", Univer-
sity of Chicago, 2009.
121. \Rigidity of nearly hyperbolic metrics", University of Pennsylvania,
2009.
122. \Unbounded groups", Ecole Polytechnique, France, 2009.
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123. \Boundary rigidity and embeddings into L1, Lille University,
France, 2009.
116. Colloquium, Michigan State University, 2009.
125. \On topological aspects of the Dvoretzky Theorem", University of
Washington, 2009.
125. Colloquium, University of Toronto, 2010.
126. A plenary talk the "3G" Conference, Padre Island, Texas, 2010.
127. Colloquium, Capital Normal University, Beijing, 2010.
128. Colloquium, Polytechnic University, NYC, NY, 2010.
129. A series of 5 lectures for graduate students, San-Yat Sen University,
Guangzhou, 2010.
130. Colloquium, San-Yat Sen University, Guangzhou, 2010.
131. Colloquium, A&M Texas, 2010.
132. \Non-integrable Dvoretzky Theorem", Rokhlin's Memorial, St. Pe-
tersburg, 2010.
123. A plenary talk at the "3G" Conference, Padre Island, Texas, 2010.
134. A course of 5 lectures, a school on Geometric Measure Theory and
Analysis in Metric spaces, Pisa, Italy, 2011.
135. Colloquium, Vanderbilt University, 2011.
136. Seminar Lecture, Vanderbilt University, 2011.
137. Seminar Lecture, Princeton University, 2011.
138. Colloquium, Poly University of NYC, 2011.
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139. Seminar lecture, NYU, 2011.
140. A course of 4 lectures, Fields Institute, a school on Inverse Prob-
lems, 2012.
141. A Plenary Lecture, International Conference dedicated to 100 Years
of A.D. Alexandrov, St. Petersburg, 2012.
142. Colloquium and a Seminar Lecture, Montreal, 2012.
143. Colloquium and a Seminar Lecture, MIT, 2012.
144. University of Pennsylvania, Geometry Seminar, 2012.
145. University of Toronto, Geometry Seminar, 2012.
146. University of Washington, 2012.
147. Courant Institute, NYU, 2013.
148. Colloquium, Poly NY, 2013.
149. Seminar talk, Kent University, 2013.
150. Seminar Talk, Steklov Institute, St. Petersburg University, 2013.
151. Tel Aviv University, 2013.
152. Notre Dame University, a conference in the memory of J. Cao, 2013.
153. Systolic Geometry,, Topology, and beyond. Montpelier, France,
2014.
154. Representations, geometry, dynamics and beyond, Euler institute,
Russia, 2014.
155. Geometry and Dynamics of Finsler Manifolds, Lumini, France,
20014.
19
156. Inverse problems, Euler institute, Russia, 2014.
157. A series of four talks at \Discrete networks: geometry, dynamics
and PDEs" at Pittsburgh University, 2014.
158. Seminar Talk, U. Chicago 2014.
159. Seminar talk, Ohio State U. 2014.
160. Seminar talk.UPenn, 2014.
161. A conference at U Chicago, 2015.
162. A Colloquium at U Toronto, 2015.
163. A seminar at U Toronoto, 2015.
164. A talk at U. Chicago, 2015.
165. A talk at U. Toronto, 2015.
166. A Colloquium at U. Toronto, 2015.
167. Colloquium, University College of London, 2016
168.Colloquium, Technion, Israel, 2016
169. Colloquium, Steklov Institute, St. Petersburg, 2016.
170. Tel Aviv University, Israel, 2016.
171. Princeton University, 1:30 min lecture.2017
172. Rutgers, Colloquium. 2017
173. UPenn, Seminar talk.2017
174. Georg Washington University, Colloquium. 2017
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175. Kent University, Seminar talk.2017.
176. Akron University, Colloquium.2017.
177. University of Michigan (Ann Arbor), Seminar talk.2017
178. Duke University, Seminar talk. 2017
179. UNC, seminar talk 2017.
180. MASS Colloquium, PSU. 2017.
181. U Florida, Colloquium. 2017
182. Georgia Tech, Colloquium. 2017
183. NYU Tandon School of Engineering, Colloquium. 2017
184. Univ. of Maryland, two 1-hour talks. 2017
185. Seminar lecture, Stanford University, 2018.
186. Colloquium, Stanford University, 2018.
187. Seminar-Colloquium, UCLA, 2018.
188, Colloquium, U. San Diego, 2018.
189. Colloquium, U. Irvine, 2018.
190. A seminar talk, U. San. Diego, 2018.
191. A three-hour lecture, U. Riverside, 2018.
192. Colloquium, PSU, (Accompanied by two supporting talks), 2019.
193. An invited Lecture at The "Rokhlin-100" International Conference,
St. Petersburg, 2019.
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194. A \slide lecture " at the conference dedicated to M. Gromovs 75th
Birthday, 2020.
195. A ZOOM lecture at the U. Chicago, 2020.
196. A ZOOM lecture at the U. Florida, scheduled for Dec. 2020 but
rescheduled for and delivered in Jan. 2021.
197. A plenary lecture, Geometry in the Large. 2021
198. A plenary lecture, "The h-principle and beyond", IAS, Princeton.
2021.
199. A Colloquium Lecture, St. Petersburg, 2022
200. A seminar lecture, The Vietoris-Rips seminar, 2022
201. Peking-SPb Colloquium, 2023
Numerous Seminar Lectures and Colloquia at Penn State and informal
lectures elsewhere.
Publication List
Book:
1. D. Burago, Yu. Burago, S. Ivanov \A course in metric geometry". Grad-
uate Studies in Mathematics, 33. American Mathematical Society, Provi-
dence, RI, 2001. xiv+415 pp.
(A Russian Translation of the book has won a RFFI grant and has been
published in 2004).
Articles Published in Referred Journals:
2. D. Burago \Unboundness of a horn with nite positive part of curva-
ture in the Euclidean space." Math. Zametki, vol. 36, no. 2, 229-237, 1984.
3. D. Burago \A new approach to the computation of the entropy of geodesic
22
ow and similar dynamical systems". Soviet Math. Doklady vol. 37, pp 1041-
1044, 1988.
4. D. Burago \Flows with positive entropy". Serial \Advances in Soviet
Mathematics" vol. 9, pp 211-216, New-York, 1992.
5. D. Burago \Periodic metrics". Serial \Advances in Soviet Mathemat-
ics" vol. 9, pp 205-211, New-York, 1992.
6. D. Burago \A Lower Bound for the SPLIT-FIND Problem for a Pointer
Machines". Journal of the St.-Petersburg Mathematical Society, Amer. Math.
Soc. Trans. (2) vol. 159, pp 23-38, 1992.
7. D. Burago, S. Ivanov "Isometric embeddings of Finsler manifolds". Al-
gebra & Analysis, vol. 5, no. 1, pp 159-169, 1993.
8. D. Burago \Periodic metrics". In Progress in Nonlinear Di erential
Equations (editor H.Brezis), pp 90-95, Birkhauser, 1993.
9. D. Burago, S. Ivanov \Riemannian Tori Without Conjugate Points are
Flat". Geometry and Functional Analysis, vol. 3 no 4, pp 259-269, 1994.
10. D. Beauquier, D. Burago, A. Slissenko \On the Complexity of Fi-
nite Memory Policies for Markov Decision Processes", in: \Mathematical
Foundation of Computer Science". Proceeding of MFCS'95", 1995, pages
191-200, \Springer Verlag", Lect. Notes in Comput. Sci, vol. 969.
11. D. Burago, S. Ivanov \On Asymptotic Volume of Tori". "Geometry
and Functional Analysis". v.5, pp 800-808, 1995.
12. D. Burago, M. DeRougemont, A. Slissenko \On the Complexity of Par-
tially Observed Markov Decision Processes", Theor. Comput. Sci., 1996,
pp 161-183. ed. A.Razborov.
13. D. Burago, S. Ivanov, B. Kleiner \On the Structure of the Stable Norm
of Periodic Metrics." Mathematical Research Letters, 4, pp 791-808, 1997
14. D. Burago, S. Ferleger, A. Kononenko \Topological Entropy of Semi-
Dispersing Billiards". Ergodic Th. & Dyn. Syst., 18, pp 1-15, 1998.
23
15. D. Burago, B. Kleiner \Separated Nets in Euclidean Space and Ja-
cobians of Bi-Lipschitz Maps".Geometric and Functional Analysis, 8, pp
273-282, 1998.
16. D. Burago, S. Ferleger, A. Kononenko \Unfoldings and Global bounds on
the Number of Collisions for Generalized Semi- Dispersing Billiards."Asian
j. of Math., 2 n. 1, pp 141-152, 1998
17. D. Burago. \Geometry of Tori: Riemannian versus Finsler?" Progress
in Mathematics, Birkhauser Verlag, v. 168, pp 132-135, 1998.
18. D. Burago, S. Ferleger, A. Kononenko \Uniform estimates on the number
of collisions in semi-dispersing billiards". Annals of Math, 147, pp 695-708,
1998.
19. D. Burago, S. Ivanov \On asymptotic isoperimetric constant of tori".
Geom. Funct. Anal. 8 (1998), no. 5, 783{787
20. D. Burago, S. Ferleger, A. Kononenko \A geometric approach to semi-
dispersing billiards". Ergodic Theory Dynam. Systems 18 (1998), no. 2,
303{319
21. D. Burago. \Hard Balls Gas and Alexandrov Spaces of Curvature
Bounded Above", Proceedings of the ICM, invited lecture, vol 2, pp 289-
298, 1998.
22. D. Burago, M. DeRougemont \On the Average-Case Complexity of
the Graph Reliablility Problem on Gaussian Distributions."Fundamentae
Informatica, vol 36 (1998), pp 307-315.
23. D. Burago, S. Ferleger, A. Kononenko \A geometric approach to semi-
dispersing billiards". Hard ball systems and the Lorentz gas, 9{27, Ency-
clopaedia Math. Sci., 101, Springer, Berlin, 2000.
24. D. Burago, S. Ferleger, A. Kononenko \Gluing copies of a 3-dimensional
polyhedron to obtain a closed nonpositively curved pseudomanifold". Proc.
Amer. Math. Soc. 129 (2001), no. 5, 1493{1498.
24
25. Burago, D.; Ferleger, S.; Kononenko, A. \Collisions in semi-dispersing
billiard on Riemannian manifold". Topology Appl. 122 (2002), no. 1-2,
87{103.
26. Burago, D.; Kleiner, B. \Rectifying separated nets". Geom. Funct.
Anal. 12 (2002), no. 1, 80{92.
27. D. Burago, S. Ivanov \Minimal surfaces in normed spaces, symplectic
llings, and asymptotic volume growth of Finsler tori". Annals of Mathe-
matics, 2002, vol.156, n. 3.
28. D. Burago, D. Grigoriev, A. Slissenko \Approximating shortest path
for the skew lines problem in time doubly logarithmic in 1/epsilon", Theo-
ret. Comput. Sci. 315 (2004), no. 2-3, 371{404
29. D. Burago, S. Ivanov \Gaussian images of surfaces and ellipticity of
volume functionals", Geom. Funct. Anal. 14 (2004), no. 3, 469{490.
30. M. Brin, D. Burago, S. Ivanov \ Partially Hyperbolic Automorphisms of
3-Manifolds with Abelian 1",in Dynamics, Geometry, and Rigidity, a col-
lection of research papers, pp. 307-312, Cambridge University Press 2004.
31. D. Burago \ Semi-dispersing Billiard Systems with In nite Topologi-
cal Entropy of Time-1 Map", Erg. Th. & Dyn. Syst. 26 (2006), no. 1,
45-52.
32. D. Burago, S. Ivanov, D. Schoenthal \Two counterexamples in low-
dimensional length geometry." \Algebra & Analysis" 19 (2007), no. 1, 46{
59. Translation in St. Petersburg Math. J. 19 (2008), no. 1, 33{43 .
33. D. Burago, S. Ivanov \A remark on the group of PL-di eomorphisms in
Dimension 1", Geometric and probabilistic structures in dynamics, 141148,
Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008.
34. D. Burago, S. Ivanov, L. Polterovich \Large groups and unbounded
quasi-semi-norms",Groups of di eomorphisms, 221250, Adv. Stud. Pure
Math., 52, Math. Soc. Japan, Tokyo, 2008.
35. D. Burago, S. Ivanov \Partially hyperbolic di eomorphisms of 3-manifolds
25
with Abelian fundamental groups", J. Mod. Dyn. 2 (2008), no. 4, 541580.
36. M. Brin, D. Burago, S. Ivanov \Dynamical Coherence of Partially Hy-
perbolic Di eomorphisms of the 3-Torus", J. Mod. Dyn. 3 (2009), no. 1,
111.
37. D. Burago, S, Ivanov \Area Spaces: First steps", Geom. Funct. Anal.
19 (2009), no. 3, 662677.
38. D. Burago, S. Ivanov, S. Tabachnikov \Topological Aspects of the
Dvoretzky Theorem", J. Topol. Anal. 2 (2010), no. 4, 453467.
39. D. Burago, S. Ivanov \Boundary Rigidity of Metrics Close to Euclidean
ones", Annals of Math. (2) 171 (2010), no. 2, 11831211.
40. D. Burago, S. Ivanov. \On intrinsic geometry of surfaces in normed
spaces". Geom. Topol. 15 (2011), no. 4, 22752298.
41. D. Burago, S. Ivanov, \Area minimizers and boundary rigidity of al-
most hyperbolic metrics", Duke Math J. 162 (7) 1205-1248, 2013..
42. D. Burago, S. Ivanov. Minimality of planes in normed spaces. Geom.
Funct. Anal. 22 (2012), no. 3, 627638..
43. D. Burago, S. Ivanov. "Polyhedral Finsler Spaces with locally unique
geodesics", Advances in Mathematics, 247 (2013), 343-355.
44. D. Burago, S. Ivanov. \Uniform approximation of metrics by graphs",
Proc. Amer. Math. Soc. 143 (2015), no. 3, 12411256.
45. D. Burago, S. Ivanov, R. Kurylev. \Graph Laplace Approximations
for Manifolds", A graph discretization of the Laplace-Beltrami operator. J.
Spectr. Theory 4 (2014), no. 4, 675714.
46. D. Burago, S. Ivanov "Boundary distance, lens maps and local gen-
eration of entropy", Geom. Topol. 20 (2016), no. 1, 469490.
47. Introduction to (an co-editing of) Gromov's part of the Abel Winners
volume.
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48. D. Burago. My dad: an engineer in mathematics and life. In a special
volume of St. Petersburg Journal dedicated to the 80th birthday of Yu.
Burago" (2018), no. 1.
49. D. Burago On several problems posed by H. Busemann and related
to Geometry in normed spaces, in Collected works of H. Busemann, Vol II,
2018.
50.D. Burago, S. Ivanov, A. Novikov. A survival guide for a feeble sh.
St. Petersburg Math. J. 29 (2018), no. 1, 3341.
51. D. Burago, J. Lu, T. Ozuch, How large isotopy is needed to connect
homotopic di eomorphisms of 2. J. Topol. Anal. 12 (2020).
52. Burago, Dmitri; Ivanov, Sergei; Kurylev, Yaroslav. Spectral stabil-
ity of metric-measure Laplacians. Israel J. Math. 232 (2019), no. 1, 125158.
54. Burago, Dmitri; Ivanov, Sergei; Kurylev, Yaroslav. Spectral stability of
metric-measure Laplacians. Israel J. Math. 232 (2019), no. 1, 125158.
55. D. Burago, S. Ivanov. Examples of exponentially many collisions in a
hard ball system. Accepted to Ergodic Theory Dynamical Systems, 2020.
56. D. Burago, D. Chen. An example of C1 small perturbations of a
at 2-torus with a nondense geodesic with a given Liouville irrational rota-
tion number. Asian J. Math. 25 (2021), no. 5, 715726.
57. D. Burago, D. Chen, S. Ivanov. On total exibility of symplectic sec-
tions. Accepted to Communications in Contemporary Mathematics (CCM).
.
58. Burago, S. Ivanov, Y. Kurylev, J. Lu. Approximations of the con-
nection Laplacian spectra. Math. Z. 301 (2022), no. 3, 31853206.
59. D. Burago, S. Ivanov, M. Lassas, J. Lu. `Stability of the Gelfand In-
verse Problem via the unique continuation (to the memory of Ya. Kurylev).
Accepted to "Analysis and PDEs.
60. D. Burago, D. Chen, S. Ivanov. Key ideas behind perturbing any
27
completely integrable Hamiltonian system obtaining volume entropy non-
expansiveness. Under revision.
61. D. Burago, D. Chen, H. Qiu, J. Lu. (About 30 pp). On some un-
solved problems of geometric origin. Submitted by invitation to the volume
dedicated to A.M. Vershik of Groups, Geometry, Dynamics published by the
European Mathematical Society..
62. D. Burago, S. Ivanov \On conjugacy problem for geodesic ows without
conjugate points", in preparation.
Other:
63. D. Burago. Some memories about V. A. Zalgaller. In a book \V.A.
Zalgaller: the war and peace of a St. Petersburg mathematician, in Russian.
64. D. Burago. Essay "Academician A.D. Alexandrov", about 15 pages,
in "St. Petersburg mathematicians and their discoveries" (MCCME).
Many journal publications and ve books in Russian Literature and in Art.
Several one-man art exhibitions.
Preprints:
65. D.Burago, S. Finashin and D. Fomin \Optional course in Mathemat-
ics for grades 6{7". Leningrad State University, 32 pages, 1985 (in Russian).
66. D. Burago, S. Ferleger, B. Kleiner, and A. Kononenko. \Non-positively
Curved Ornaments".
67. D. Burago, M. de Rougemont and A. Slissenko \On the complexity
of planning of motion with uncertain deviations." Preprint of the Univer-
sity Paris-12 No. 93-01, 17 p., 1993.
68. D. Beauquier, D. Burago, A. Slissenko \On the Complexity of Markov
Strategies in Planning Motion with Uncertain Deviations". Technical report
of the University Paris-12, 12p, 1994.
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