Lutz Warnke
I am an Assistant Professor of Mathematics at Georgia Institute of Technology. My research focuses on probabilistic combinatorics and random discrete structures.
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); see also this older non-technical account.
I completed my PhD at the University of Oxford in 2012 under the supervision of Oliver Riordan.
Afterwards I was elected a junior research fellow at Peterhouse College, University of Cambridge.
I received in 2014 the Richard-Rado-Prize (German Mathematical Society), and in 2016 the Dénes König Prize (SIAM).
My research is supported by NSF grant DMS-1703516, a 2018 Sloan Research Fellowship, and a 2020 NSF CAREER award.
Selected papers:
- The phase transition in bounded-size 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), 63-103 : pdf, slides, poster
- Large girth approximate Steiner triple systems (with T. Bohman), Journal of the London Mathematical Society 100 (2019), 895-913 : pdf, slides, video
- Upper tails for arithmetic progressions in random subsets, Israel Journal of Mathematics 221 (2017), 317-365 : 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), 6439-6485 : pdf, slides
- The C_{ℓ}-free process, Random Structures and Algorithms 44 (2014), 490-526
- Explosive Percolation Is Continuous (with O. Riordan), Science 333 (2011), 322-324 : survey-video
Online video lectures:
Recent and upcoming talks/events:
- Rényi-100 - Conference celebrating the 100th anniversary of Alfréd Rényi's birth, invited session Random Graphs and Networks, Budapest (June 2022)
- New York Combinatorics Seminar (March 2021)
- Graph Theory and Combinatorics seminar, UIUC (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)
- Big Seminar by Laboratory of Combinatorial and Geometric Structures, Moscow Institute of Physics and Technology (September 2020)
- Combinatorics Seminar, Georgia Tech (August 2020)
- Bernoulli-IMS One World Symposium 2020, Session on Models in Physics + Session on Limit theorems, large deviations and extremes, Virtual (August 2020)
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)
- 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
Publications
- The phase transition in bounded-size Achlioptas processes (with O. Riordan)
Submitted, 95 pages : pdf, slides, video
- Counting extensions revisited (with M. Šileikis)
Submitted, 21 pages : pdf, video1, video2, short-video3
- Bounds on Ramsey Games via Alterations (with H. Guo)
Submitted, 9 pages : pdf
- The phase transition in the random d-process (with N. Wormald)
Manuscript, 32 pages : video1, video2, short-video3
- Prague dimension of random graphs (with H. Guo and K. Patton)
Submitted, 20 pages : pdf, slides, video
- Preferential attachment without vertex growth: emergence of the giant component (with S. Janson)
Annals of Applied Probability, accepted, 20 pages : pdf, slides
- On Wormald's differential equation method
Combinatorics, Probability and Computing, accepted, 7 pages : pdf
- Packing Nearly Optimal Ramsey R(3,t) Graphs (with H. Guo)
Combinatorica 40 (2020), 63-103 : pdf, slides, poster
- On the missing log in upper tail estimates
Journal of Combinatorial Theory Series B 140 (2020), 98-146 : 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), 895-913 : pdf, slides, video
- A Counterexample to the DeMarco-Kahn Upper Tail Conjecture (with M. Šileikis)
Random Structures and Algorithms 55 (2019) 775-794 : pdf
- Sesqui-type branching processes (with S. Janson and O. Riordan)
Stochastic Processes and their Applications 128 (2018), 3628-3655 : 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), 317-365 : pdf, slides
- The lower tail: Poisson approximation revisited (with S. Janson)
Random Structures and Algorithms 48 (2016), 219-246 : 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), 6439-6485 : pdf, slides
- On the Method of Typical Bounded Differences
Combinatorics, Probability and Computing 25 (2016), 269-299 : pdf, slides
- Convergence of Achlioptas Processes via Differential Equations with Unique Solutions (with O. Riordan)
Combinatorics, Probability and Computing 25 (2016), 154-171 : pdf, slides, survey-video
- The evolution of subcritical Achlioptas processes (with O. Riordan)
Random Structures and Algorithms 47 (2015), 174-203 : pdf, slides, survey-video
- The Janson inequalities for general up-sets (with O. Riordan)
Random Structures and Algorithms 46 (2015), 391-395 : pdf, summary-slide
- The C_{ℓ}-free process
Random Structures and Algorithms 44 (2014), 490-526 : pdf
- When does the K_{4}-free process stop?
Random Structures and Algorithms 44 (2014), 355-397 : pdf, slides
- General deletion lemmas via the Harris inequality (with R. Spöhel and A. Steger)
Journal of Combinatorics 4 (2013), 251-271 : pdf, slides
- Achlioptas process phase transitions are continuous (with O. Riordan)
Annals of Applied Probability 22 (2012), 1450-1464 : pdf, survey-video
- Achlioptas processes are not always self-averaging (with O. Riordan)
Physical Review E 86 (2012), 011129 : pdf
- Dense subgraphs in the H-free process
Discrete Mathematics 311 (2011), 2703-2707 : pdf, slides
- Explosive Percolation Is Continuous (with O. Riordan)
Science 333 (2011), 322-324 : Perspective Article (S. Janson), Math in the Media (AMS), Survey-video
Supervision: PhD Students and Postdocs
- He Guo, PhD student (ACO), since 02/2017
- Laura Eslava, Postdoc 2017-2019. Next position: tenure-track faculty at IIMAS-UNAM, Mexico City
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 (2017-present)
- Mathematics Departmental Colloquium, Georgia Tech (2017-2019)
Teaching
I received the Class of 1940 Course Survey Effectiveness Award in 2018,
and was a Class of 1969 Teaching Fellow in 2018-2019.
Talks
- Graph Theory and Combinatorics seminar, UIUC (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)
- Bernoulli-IMS One World Symposium 2020, Session on Models in Physics + Session on Limit theorems, large deviations and extremes, Virtual (August 2020); short-video1, short-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 Analysis-Probability, 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, Goethe-Universität 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
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6
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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, Goethe-Universität 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)
- Rhein-Main Kolloquium Stochastik, Goethe-Universität 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)
- DMV-Jahrestagung 2015: Random Discrete Structures and Processes (invited minisymposium), University of Hamburg (September 25, 2015)
- Symposium on Fluctuation driven phenomena in non-equilibrium statistical mechanics, University of Warwick (September 23, 2015)
- Workshop on Extremal and Probabilistic Combinatorics, University of Birmingham (September 22, 2015)
- LMS-EMS 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, Goethe-Universität Frankfurt am Main (May 14, 2014)
- Symposium Diskrete Mathematik 2014 (Richard-Rado-Prize lecture), Frankfurt am Main (May 10, 2014); [Richard-Rado-Prize]
- 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 One-Day 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 Mini-Conference, 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)
- Warwick-Weizmann 2011 Workshop, University of Warwick (September 15, 2011)
- Memphis-Budapest 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-)Doc-Course Mini-Conference, 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