Lutz Warnke
I am an Associate Professor of Mathematics at UC San Diego.
I'm particularly interested in random graphs and processes, phase transitions, and combinatorial probability (as well as applications thereof to extremal combinatorics, Ramsey theory, and related areas).
I completed my PhD at the University of Oxford in 2012 under the supervision of Oliver Riordan.
Afterwards I was a elected junior research fellow at Peterhouse College, University of Cambridge.
I subsequently received tenure at Georgia Institute of Technology.
I received in 2014 the RichardRadoPrize (German Mathematical Society),
in 2016 the Dénes König Prize (SIAM),
in 2018 a Sloan Research Fellowship,
and in 2020 a NSF CAREER award.
Selected papers:
 The phase transition in boundedsize Achlioptas processes (with O. Riordan), submitted, 95 pages : pdf, slides, video
 Packing nearly optimal Ramsey R(3,t) graphs (with H. Guo), Combinatorica 40 (2020), 63103 : pdf, slides, poster
 Large girth approximate Steiner triple systems (with T. Bohman), Journal of the London Mathematical Society 100 (2019), 895913 : pdf, slides, video
 Upper tails for arithmetic progressions in random subsets, Israel Journal of Mathematics 221 (2017), 317365 : pdf, slides
 The typical structure of sparse K_{r+1}free graphs (with J. Balogh, R. Morris and W. Samotij), Transactions of the AMS 368 (2016), 64396485 : pdf, slides
 The C_{ℓ}free process, Random Structures and Algorithms 44 (2014), 490526
 Explosive Percolation Is Continuous (with O. Riordan), Science 333 (2011), 322324 : surveyvideo
Online video lectures:
 The degreerestricted random process is far from uniform (2022, Simons Institute Berkeley)
 Prague Dimension of Random Graphs (2021, New York Combinatorics Seminar)
 Counting extensions in Random Graphs (2020, Extremal and Probabilistic Combinatorics Webinar)
 The phase transition in the random dprocess (2019, Moscow Institute of Physics and Technology)
 Large girth approximate Steiner triple systems (2018, Georgia Tech)

Lectures on Random Graph Processes:
1
2
3
4
5
6
7
8
9 10
(2017, The Fields Institute, Summer School on Random Graphs and Probabilistic Methods)
 The phase transition in boundedsize Achlioptas processes (2016, University of Texas at Austin)
 The lower tail: Poisson approximation revisited (2016, Simons Institute Berkeley)
 Survey: The evolution of Achlioptas processes (2012, Banff)
Recent and upcoming talks/events:
 Workshop Random Graphs: Combinatorics, Complex Networks and Disordered Systems, MFO, Oberwolfach (March 2023)
 Workshop Analytic and Probabilistic Combinatorics, BIRS, Banff (November 2022)
 Workshop Graph Limits, Nonparametric Models, and Estimation, Simons Institute Berkeley (September 2022)
 Workshop Combinatorial Geometry and Ramsey Theory, San Diego (September 2022)
 Third Southwestern German Workshop on Graph Theory, Heidelberg (June 2022)
 Rényi100  Conference celebrating the 100th anniversary of Alfréd Rényi's birth, invited session Random Graphs and Networks, Budapest (June 2022)
 Combinatorics Seminar, UC San Diego (May 2022)
 Graph Theory Seminar, Georgia Tech (May 2022)
 Workshop Combinatorics, Probability and Computing, MFO, Oberwolfach (April 2022)
 LUNUUMN Joint Probability Seminar (March 2022)
 Codes and Expansions (CodEx) Seminar, Virtual (January 2022)
Publications
 The phase transition in boundedsize Achlioptas processes (with O. Riordan)
Submitted, 95 pages : pdf, slides, video
 The degreerestricted random process is far from uniform (with M. Molloy and E. Surya)
Submitted, 32 pages : pdf, slides, video
 On the concentration of the chromatic number of random graphs (with E. Surya)
Submitted, 12 pages : pdf, slides
 The Density of Costas Arrays Decays Exponentially (with B. Correll and C. Swanson)
Submitted, 7 pages : pdf, slides, video
 Bounds on Ramsey Games via Alterations (with H. Guo)
Submitted, 9 pages : pdf, slides
 The phase transition in the random dprocess (with N. Wormald)
Manuscript, 32 pages : pdf, video, shortvideo
 On the typical structure of graphs not containing a fixed vertexcritical subgraph (with O. Engelberg and W. Samotij)
Submitted, 53 pages : pdf
 Prague dimension of random graphs (with H. Guo and K. Patton)
Combinatorica, accepted, 20 pages : pdf, slides, video
 The jump of the clique chromatic number of random graphs (with L. Lichev and D. Mitsche)
Random Structures and Algorithms, accepted, 14 pages : pdf, slides
 On Wormald's differential equation method
Combinatorics, Probability and Computing, accepted, 7 pages : pdf
 Counting extensions revisited (with M. Šileikis)
Random Structures and Algorithms 61 (2022) 330 : pdf, video, shortvideo
 On the power of random greedy algorithms (with H. Guo)
European Journal of Combinatorics 105 (2022), 103551 : pdf, slides
 Preferential attachment without vertex growth: emergence of the giant component (with S. Janson)
Annals of Applied Probability 31 (2021), 15231547 : pdf, slides
 Note on Sunflowers (with T. Bell and S. Chueluecha)
Discrete Mathematics 344 (2021), 112340 : pdf, REU 2020 slides
 Packing Nearly Optimal Ramsey R(3,t) Graphs (with H. Guo)
Combinatorica 40 (2020), 63103 : pdf, slides, poster
 On the missing log in upper tail estimates
Journal of Combinatorial Theory Series B 140 (2020), 98146 : pdf, slides
 Upper Tail Bounds for Stars (with M. Šileikis)
The Electronic Journal of Combinatorics 27 (2020), Paper 1.67, 23pp : pdf
 Large girth approximate Steiner triple systems (with T. Bohman)
Journal of the London Mathematical Society 100 (2019), 895913 : pdf, slides, video
 A Counterexample to the DeMarcoKahn Upper Tail Conjecture (with M. Šileikis)
Random Structures and Algorithms 55 (2019) 775794 : pdf, slides
 Sesquitype branching processes (with S. Janson and O. Riordan)
Stochastic Processes and their Applications 128 (2018), 36283655 : pdf
 On the critical probability in percolation (with S. Janson)
Electronic Journal of Probability 23 (2018), Paper 1, 25pp : pdf
 Upper tails for arithmetic progressions in random subsets
Israel Journal of Mathematics 221 (2017), 317365 : pdf, slides
 The lower tail: Poisson approximation revisited (with S. Janson)
Random Structures and Algorithms 48 (2016), 219246 : pdf, slides, video
 The typical structure of sparse K_{r+1}free graphs (with J. Balogh, R. Morris and W. Samotij)
Transactions of the AMS 368 (2016), 64396485 : pdf, slides
 On the Method of Typical Bounded Differences
Combinatorics, Probability and Computing 25 (2016), 269299 : pdf, slides
 Convergence of Achlioptas Processes via Differential Equations with Unique Solutions (with O. Riordan)
Combinatorics, Probability and Computing 25 (2016), 154171 : pdf, slides, surveyvideo
 The evolution of subcritical Achlioptas processes (with O. Riordan)
Random Structures and Algorithms 47 (2015), 174203 : pdf, slides, surveyvideo
 The Janson inequalities for general upsets (with O. Riordan)
Random Structures and Algorithms 46 (2015), 391395 : pdf, summaryslide
 The C_{ℓ}free process
Random Structures and Algorithms 44 (2014), 490526 : pdf
 When does the K_{4}free process stop?
Random Structures and Algorithms 44 (2014), 355397 : pdf, slides
 General deletion lemmas via the Harris inequality (with R. Spöhel and A. Steger)
Journal of Combinatorics 4 (2013), 251271 : pdf, slides
 Achlioptas process phase transitions are continuous (with O. Riordan)
Annals of Applied Probability 22 (2012), 14501464 : pdf, surveyvideo
 Achlioptas processes are not always selfaveraging (with O. Riordan)
Physical Review E 86 (2012), 011129 : pdf
 Dense subgraphs in the Hfree process
Discrete Mathematics 311 (2011), 27032707 : pdf, slides
 Explosive Percolation Is Continuous (with O. Riordan)
Science 333 (2011), 322324 : Perspective Article (S. Janson), Math in the Media (AMS), Surveyvideo
Supervision: PhD Students, Postdocs and Undergraduate Students
 Erlang Surya, PhD student, since 2020
 He Guo, PhD student 20172021. Placement: postdoc at Technion, Israel
 Laura Eslava, Postdoc 20172019. Placement: tenuretrack faculty at IIMASUNAM Mexico City, Mexico
 Kalen Patton, Undergraduate student, Fall 2019  Spring 2021. Placement: PhD program in ACO at Georgia Tech (Algorithms, Combinatorics and Optimization)
 Tolson Bell, Undergraduate student, REU 2020. Placement: PhD program in ACO at Carnegie Mellon University (Algorithms, Combinatorics and Optimization)
 Petch Chueluecha, Undergraduate student, REU 2020. Placement: PhD program at University of Virginia (Number Theory and Combinatorics)
 Chidozie Onyeze, Undergraduate student, Summer 2021. Placement: Microsoft (Software Engineering)
Organization
 Atlanta Math Teachers Circle: Summer Workshop (Georgia Tech, 07/2019); Photo
 Special Session on Random Discrete Structures (AMS Fall Southeastern Meeting, Virtual, 10/2020):
Special Session on Random Discrete Structures (SIAM Conference on Discrete Mathematics, Portland, 06/2020): canceled due to Coronavirus
Special Session on Random Discrete Structures (AMS Eastern Sectional Meeting, Tufts University, 03/2020): canceled due to Coronavirus
 Invited Minisymposium on Random Graphs (CanaDAM 2019: 7th Canadian Discrete and Algorithmic Mathematics Conference, Simon Fraser University, 05/2019)
 Special Session on Random Discrete Structures (AMS Southeastern Sectional Meeting, Auburn University, 03/2019)
 Special Session on Random Discrete Structures (AMS Southeastern Sectional Meeting, Vanderbilt University, 04/2018)
 Combinatorics Seminar, Georgia Tech (20172021)
 Mathematics Departmental Colloquium, Georgia Tech (20172019)
Teaching
I received the Student Recognition of Excellence in Teaching: Class of 1934 Award in 2020, and the Class of 1940 Course Survey Effectiveness Award in 2018; I also was a Class of 1969 Teaching Fellow in 20182019.
Talks
 Workshop Graph Limits, Nonparametric Models, and Estimation, Simons Institute Berkeley (September 2022); video
 Workshop Combinatorial Geometry and Ramsey Theory, San Diego (September 2022)
 Third Southwestern German Workshop on Graph Theory (plenary speaker), Heidelberg (June 2022)
 Rényi100  Conference celebrating the 100th anniversary of Alfréd Rényi's birth, invited session Random Graphs and Networks, Budapest (June 2022)
 Combinatorics Seminar, UC San Diego (May 2022)
 Graph Theory Seminar, Georgia Tech (May 2022)
 Workshop Combinatorics, Probability and Computing, MFO, Oberwolfach (April 2022)
 LUNUUMN Joint Probability Seminar (March 2022)
 Codes and Expansions (CodEx) Seminar, Virtual (January 2022); video
 DIMAP Seminar, Warwick (November 2021)
 CMSA Combinatorics and Probability Seminar, Harvard (November 2021)
 CMSA seminar, Combinatorial Mathematics Society of Australasia (November 2021)
 "BCC 2021": 28th British Combinatorial Conference (July 2021)
 Oberseminar Algebra und Geometrie OttovonGuerickeUniversität Magdeburg (July 2021)
 Permutation Patterns 2021 Virtual Workshop (June 2021)
 "AofA2021": 32nd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (June 2021); video
 Colloquium, UC San Diego (June 2021)
 RandNET Seminar, MSCARISE Randomness and Learning in Networks (May 2021)
 SCMS Combinatorics Seminar, Shanghai Center for Mathematical Sciences (May 2021); video
 Graz Combinatorics and Optimization Seminar, TU Graz (March 2021)
 New York Combinatorics Seminar, New York (March 2021); video
 Combinatorics Seminar, Warwick (February 2021)
 Virtual CombinaTexas 2021, Texas A&M University (February 2021)
 Graph Theory and Combinatorics seminar, University of Illinois at UrbanaChampaign (December 2020)
 AMS Sectional Meeting (Fall Southeastern), Special Session on Structural and Extremal Graph Theory, Virtual (October 2020)
 Probabilistic Combinatorics Online 2020 (Plenary Speaker), Virtual (September 2020); video
 Big Seminar by Laboratory of Combinatorial and Geometric Structures, Moscow Institute of Physics and Technology (September 2020); video
 Combinatorics Seminar, Georgia Tech (August 2020)
 BernoulliIMS One World Symposium 2020, Session on Models in Physics + Session on Limit theorems, large deviations and extremes, Virtual (August 2020); video1, video2
Foundations of Computational Mathematics (FoCM), Workshop Graph Theory and Combinatorics, Vancouver (June 2020): canceled due to Coronavirus
SIAM Conference on Discrete Mathematics, Special Session on Random Discrete Structures, Portland (June 2020): canceled due to Coronavirus
 Extremal and Probabilistic Combinatorics Webinar, Virtual (May 2020); video
 School of Mathematics Colloquium, Georgia Tech (May 2020)
Workshop Random Graphs: Combinatorics, Complex Networks and Disordered Systems, MFO, Oberwolfach (May 2020): canceled due to Coronavirus
ACO Student Seminar Georgia Tech (April 2020): canceled due to Coronavirus
Combinatorics Seminar, Georgia Tech (March 2020): canceled due to Coronavirus
AMS Sectional Meeting (Spring Eastern), Special Session on Random Discrete Structures, Tufts University (March 2020): canceled due to Coronavirus
 STEM Teachers @ Tech Day, Atlanta Science Festival (March 2020)
 Intown Atlanta Math Teachers Circle (February 2020)
 Combinatorics Seminar, Georgia Tech (Janauary 2020)
 Oberseminar Diskrete Mathematik und Algebra, TU Ilmenau (December 2019)
 Oberseminar AnalysisProbability, Max Planck Institute/Leipzig University (December 2019)
 Machine Learning Crash Course and Workshop, Georgia Tech (December 2019)
 AMS Sectional Meeting (Fall Southeastern), Special Session on Extremal and Probabilistic Combinatorics, University of Florida, Gainesville (November 2019)
 Intown Atlanta Math Teachers Circle Summer Workshop (July 2019)
 "CanaDAM 2019": 7th Canadian Discrete and Algorithmic Mathematics Conference, Invited Minisymposium Random Graphs, Vancouver (May 2019)
 Workshop on graphs, networks, and their applications (plenary speaker), Moscow Institute of Physics and Technology (May 2019); video
 Combinatorics Seminar, Emory University (April 2019)
 Research Horizons Seminar, Georgia Tech (April 2019)
 Workshop on Combinatorics, Probability and Computing, MFO, Oberwolfach (April 2019)
 Intown Atlanta Math Teachers Circle (March 2019)
 AMS Sectional Meeting (Spring Southeastern), Special Session on Random Discrete Structures, Auburn University (March 2019)
 Analysis Seminar, Stony Brook University (March 2019)
 Oberseminar Wahrscheinlichkeitstheorie, LMU/TUM Munich (December 2018)
 Stochastics and Statistics Seminar, MIT (December 2018)
 Recent Advances in Extremal Combinatorics, Oxford (December 2018)
 Combinatorics Seminar (GANTC), The University of North Carolina at Greensboro (November 2018)
 Discrete Mathematics Seminar, Virginia Commonwealth University (November 2018)
 Combinatorics Seminar, Georgia Tech (September 2018); video
 Stochastics Colloquium, TU Eindhoven (August 2018)
 12th International Vilnius Conference on Probability Theory and Mathematical Statistics, Invited Session on Random Graphs, Vilnius (July 2018)
 40th Stochastic Processes and their Applications International Conference, Invited Session on Criticality and other topological issues of random graphs, Gothenburg (June 2018)
 Graph Theory and Combinatorics Seminar, Vanderbilt University (April 2018)
 Colloquium, Georgia State University (March 2018)
 T+UHH Research Seminar, Hamburg University of Technology (December 2017)
 Workshop on Network Models: Structure and Function, MFO, Oberwolfach (December 2017)
 Combinatorics Seminar, FU Berlin (December 2017)
 Oberseminar Diskrete Mathematik, GoetheUniversität Frankfurt am Main (December 2017)
 Combinatorics Seminar, Emory University (October 2017)
 Workshop on Randomness and Graphs: Processes and Structures, EURANDOM, Eindhoven (September 2017)
 "RSA 2017": 16th International Conference on Random Structures and Algorithms, Gniezno (August, 2017)
 Mathematical Congress of the Americas (MCA): Extremal and Probabilistic Combinatorics, McGill University, Montreal (July 2017)
 Random Discrete Structures and Beyond Workshop, Barcelona (June 2017)
 Summer School on Random Graphs and Probabilistic Methods (10 lectures), Fields Institute, Toronto (May  June 2017); [videos: 1
2
3
4
5
6
7
8
9 10]
 Stochastics Seminar, Georgia Tech (April 2017)
 Research Horizons Seminar, Georgia Tech (April 2017)
 ACO Student Seminar, Georgia Tech (April 2017)
 Combinatorics & Probability seminar, Ohio State University (March 2017)
 ACO Seminar, Carnegie Mellon University (February 2017)
 ACO25 Conference: Celebrating the 25th Anniversary of the ACO Program (Plenary Speaker), Georgia Tech, Atlanta (January 2017)
 Noon seminar, Charles University, Prague (December 2016)
 Combinatorics Seminar, University of Birmingham (December 2016)
 ACO Seminar, Georgia Tech, Atlanta (November 15, 2016)
 Combinatorics Seminar, University of Bristol (October 25, 2016)
 Theoretical Foundations for Statistical Network Analysis Seminar, Isaac Newton Institute, Cambridge (September 29, 2016); video
 6th Polish Combinatorial Conference (plenary speaker), Bedlewo (September 21, 2016)
 Combinatorics Seminar, Georgia Tech, Atlanta (August 26, 2016)
 Workshop on Phase transitions in discrete structures, GoetheUniversität Frankfurt am Main (July 26, 2016)
 Discrete Mathematics Days, Barcelona (July 7, 2016)
 Probabilistic and Extremal Combinatorics Downunder, Monash University, Melbourne (June 15, 2016)
 SIAM Conference on Discrete Mathematics (invited minisymposium), Georgia State University (June 10, 2016)
 SIAM Conference on Discrete Mathematics (Dénes König Prize lecture), Georgia State University (June 7, 2016); [Dénes König Prize]
 Discrete Mathematics Seminar, Monash University, Melbourne (May 23, 2016)
 Workshop on Random Graph Processes, University of Texas at Austin (May 9, 2016); video
 Random Instances and Phase Transitions, Simons Institute Berkeley (May 5, 2016); video
 Combinatorics Seminar, University of Cambridge (February 18, 2016)
 RheinMain Kolloquium Stochastik, GoetheUniversität Frankfurt am Main (January 22, 2016)
 Probability Seminar, University of Cambridge (November 24, 2015)
 Atlanta Lecture Series in Combinatorics and Graph Theory, Georgia Tech (November 14, 2015)
 Combinatorics Seminar, Emory University (November 13, 2015)
 Probability Seminar, University of Bath (October 19, 2015)
 DIMAP Seminar, University of Warwick (October 13, 2015)
 DMVJahrestagung 2015: Random Discrete Structures and Processes (invited minisymposium), University of Hamburg (September 25, 2015)
 Symposium on Fluctuation driven phenomena in nonequilibrium statistical mechanics, University of Warwick (September 23, 2015)
 Workshop on Extremal and Probabilistic Combinatorics, University of Birmingham (September 22, 2015)
 LMSEMS Mathematical Weekend, Birmingham (September 19, 2015)
 Logic and Random Graphs, Lorentz Center Leiden (September 4, 2015)
 "RSA 2015": 17th International Conference on Random Structures and Algorithms, Carnegie Mellon University (July 31, 2015)
 Algorithmic Perspective in Economics and Physics Seminar, Centre de Recerca Matemàtica, Barcelona (June 17, 2015)
 "AofA 2015": 26th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (plenary speaker), Strobl (June 9, 2015)
 "CanaDam 2015": 5th biennial Canadian Discrete and Algorithmic Mathematics Conference (invited minisymposium), University of Saskatchewan (June 3, 2015)
 STAR Workshop on Random Graphs, Radboud University Nijmegen (April 9, 2015)
 The 4th Joint British Mathematical Colloquium (invited minisymposium), University of Cambridge (March 30, 2015)
 Combinatorics Seminar, University of Birmingham (February 19, 2015)
 Stochastic Analysis Seminar, University of Oxford (October 27, 2014)
 Combinatorics Seminar, University of Oxford (June 10, 2014)
 Oberseminar Diskrete Mathematik, GoetheUniversität Frankfurt am Main (May 14, 2014)
 Symposium Diskrete Mathematik 2014 (RichardRadoPrize lecture), Frankfurt am Main (May 10, 2014); [RichardRadoPrize]
 Symposium on Phase transitions in discrete structures and computational problems, University of Warwick (May 5, 2014)
 Combinatorics Seminar, University of Cambridge (March 13, 2014)
 Workshop on Probability and Graphs, EURANDOM, Eindhoven (January 10, 2014)
 DIMAP Seminar, University of Warwick (December 3, 2013)
 Combinatorics Seminar, University of Bristol (October 31, 2013)
 The Kelvin Club (general audience talk), Peterhouse, University of Cambridge (October 15, 2013)
 Discrete Mathematics Seminar, Monash University, Melbourne (September 16, 2013)
 "RSA 2013": 16th International Conference on Random Structures and Algorithms, Poznan (August 9, 2013)
 Workshop Analysis on Graphs and its Applications, Loughborough University (June 25, 2013)
 Discrete Mathematics Seminar, Adam Mickiewicz University, Poznan (June 11, 2013)
 Workshop on Combinatorics and Probability, MFO, Oberwolfach (April 16, 2013)
 STAR Workshop on Random Graphs, University of Utrecht (November 2, 2012)
 New Trends and Directions in Combinatorics workshop, BIRS, Banff (August 20, 2012); video
 Theory Seminar, Microsoft Research, Redmond (July 13, 2012)
 Two OneDay Colloquia in Combinatorics (plenary speaker), Queen Mary, University of London, (Mai 16, 2012)
 Workshop on Probabilistic techniques in Graph Theory, University of Birmingham (March 26, 2012)
 MDS Block Course MiniConference, FU Berlin (March 9, 2012)
 Combinatorics Seminar, University of Cambridge (March 1, 2012)
 Pure mathematics seminar, Royal Holloway, University of London (February 21, 2012)
 Combinatorics Seminar, University of Oxford (January 31, 2012)
 CABDyN Network Journal Club, University of Oxford (December 1, 2011)
 Combinatorics Seminar, University of Birmingham (November 17, 2011)
 WarwickWeizmann 2011 Workshop, University of Warwick (September 15, 2011)
 MemphisBudapest Summer School in Combinatorics, Budapest (August 15, 2011)
 "RSA 2011": 15th International Conference on Random Structures and Algorithms, Atlanta (May 25, 2011)
 DIMAP Seminar, University of Warwick (May 17, 2011)
 Combinatorics Seminar, University of Oxford (May 10, 2011)
 Mittagsseminar, ETH Zürich (April 28, 2011)
 Combinatorics Seminar, University of Oxford (February 8, 2011)
 MDS (Pre)DocCourse MiniConference, FU Berlin (October 15, 2010)
 Combinatorics Seminar, University of Memphis (October 8, 2010)
 DIMAP Workshop on Extremal and Probabilistic Combinatorics, Petersfield (July 23, 2010)
 21st Postgraduate Combinatorics Conference, Queen Mary, University of London (July 7, 2010)
 Young Researchers in Mathematics 2010, University of Cambridge (March 27, 2010)
 Mittagsseminar, ETH Zürich (December 17, 2009)
 Mittagsseminar, ETH Zürich (September 9, 2009)
Contact details