lutz warnke

publications | google scholar | teaching | supervision | organization | talks | contact

i am an associate professor of mathematics at uc san diego. i am 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 am looking for highly motivated phd 2022年亚洲世界杯预选赛 and postdocs.

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 richard-rado-prize (german mathematical society), in 2016 the dénes könig prize (siam), in 2018 a sloan research fellowship, and in 2020 a nsf career award.

i co-organize the combinatorics seminar at uc san diego. if you would like to give a talk, please send me an email.

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
• on wormald's differential equation method, combinatorics, probability and computing, accepted, 7 pages : pdf
• 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
• on the method of typical bounded differences, combinatorics, probability and computing 25 (2016), 269-299 : 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:

• the degree-restricted 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 d-process (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 bounded-size 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)

• the phase transition in bounded-size achlioptas processes (with o. riordan)
  submitted, 95 pages : pdf, slides, video
• extreme local statistics in random graphs: maximum tree extension counts (with p. araújo, s. griffiths and m. Šileikis)
  submitted, 38 pages : pdf
• two-point concentration of the domination number of random graphs (with t. bohman and e. zhu)
  submitted, 16 pages : pdf, slides
• local limit of the random degree constrained process (with b. ráth and m. szőke)
  submitted, 53 pages : pdf
• the clique chromatic number of sparse random graphs (with m. fernandez v)
  submitted, 24 pages : pdf
• the phase transition in the random d-process (with n. wormald)
  submitted, 32 pages : pdf, video, short-video
• the degree-restricted random process is far from uniform (with m. molloy and e. surya)
  submitted, 32 pages : pdf, slides, video
• isomorphisms between dense random graphs (with e. surya and e. zhu)
  submitted, 26 pages : pdf, slides
• on wormald's differential equation method
  combinatorics, probability and computing, accepted, 7 pages : pdf
• on the typical structure of graphs not containing a fixed vertex-critical subgraph (with o. engelberg and w. samotij)
  random structures and algorithms 65 (2024), 644-702 : pdf
• note on down-set thresholds
  random structures and algorithms 64 (2024), 807-813 : pdf
• on the concentration of the chromatic number of random graphs (with e. surya)
  the electronic journal of combinatorics 31 (2024), paper 1.44, 18pp : pdf, slides
• prague dimension of random graphs (with h. guo and k. patton)
  combinatorica 43 (2023), 853-884 : pdf, slides, video
• lagrange inversion formula by induction (with e. surya)
  the american mathematical monthly 130 (2023), 944-948 : pdf
• bounds on ramsey games via alterations (with h. guo)
  journal of graph theory 104 (2023), 470-484 : pdf, slides
• the jump of the clique chromatic number of random graphs (with l. lichev and d. mitsche)
  random structures and algorithms 62 (2023), 1016-1034 : pdf, slides
• the density of costas arrays decays exponentially (with b. correll and c. swanson)
  ieee transactions on information theory 69 (2023), 575-581 : pdf, slides, video
• counting extensions revisited (with m. Šileikis)
  random structures and algorithms 61 (2022), 3-30 : pdf, video, short-video
• 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), 1523-1547 : pdf, slides
• note on sunflowers (with t. bell and s. chueluecha)
  discrete mathematics 344 (2021), 112340 : pdf, slides
• 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, slides
• 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 k₄-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), survey-video

• matthew cho, phd ongoing
• erlang surya, phd ongoing (expected graduation spring 2025)
• emily zhu, phd completed (expected posthumous graduation 2025; thesis: topics in random graph theory and ramsey theory)
• he guo, phd 2021. placement: postdoc at technion (israel) and umea university (sweden)
• laura eslava, postdoc 2017-2019. placement: tenure-track faculty at iimas-unam mexico city, mexico
• zhengyun nie, undergraduate, summer 2022. placement: phd program at purdue university (computer science)
• chidozie onyeze, undergraduate, summer 2021. placement: phd program at cornell university (computer science)
• tolson bell, undergraduate, reu 2020. placement: phd program at carnegie mellon university (algorithms, combinatorics and optimization)
• petch chueluecha, undergraduate, reu 2020. placement: phd program at university of virginia (number theory and combinatorics)
• kalen patton, undergraduate, fall 2019 - spring 2021. placement: phd program at georgia tech (algorithms, combinatorics and optimization)

• atlanta math teachers circle: summer workshop (georgia tech, 07/2019); photo
• evolving random structures and interactions, birs worshop 26w5652. banff, canada (12/2026)
• special session on random structures, computation, and statistical inference (ams western sectional meeting, san francisco state university, 05/2024)
• 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, ucsd (2023-) and georgia tech (2017-2021)
• mathematics departmental colloquium, georgia tech (2017-2019)

• probabilistic methods in combinatorics (ucsd and georgia tech): winter 2024, spring 2021, spring 2020, spring 2018, spring 2017
• combinatorics (ucsd): fall 2024, fall 2022
• graph theory (ucsd): fall 2024, fall 2023, winter 2022
• stochastic processes (ucsd and georgia tech): spring 2025, fall 2019, fall 2018
• combinatorial statistics (ucsd): spring 2024
• modern counting techniques (ucsd): spring 2022
• enumerative combinatorics (georgia tech): fall 2020
• random discrete structures (georgia tech): fall 2017
• topics in random graphs (university of cambridge): lent term 2014-15
• concentration in discrete random processes (university of cambridge): michaelmas term 2013-14
• summer school: 10 lectures on random graph processes (fields institute, toronto): summer 2017; videos: 1 2 3 4 5 6 7 8 9 10

• analysis and probability seminar, indian institute of science, bengalore (july 2024)
• probability seminar, uc san diego (june 2024)
• combinatorics seminar, uc san diego (june 2024)
• ams sectional meeting (spring western), special session on extremal combinatorics and connections, san francisco state university, gainesville (may 2024)
• ams sectional meeting (spring western), special session on random structures, computation, and statistical inference, san francisco state university, gainesville (may 2024)
• aco seminar, carnegie mellon university (march, 2024)
• workshop on random graphs, tu dortmund (september, 2023)
• rsa 2023: 17th international conference on random structures and algorithms, carnegie mellon university (june, 2023)
• canadam 2023: canadian discrete and algorithmic mathematics conference (june 2023)
• combinatorics seminar, uc san diego (june 2023)
• 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); video
• workshop combinatorial geometry and ramsey theory, san diego (september 2022)
• third southwestern german workshop on graph theory (plenary speaker), heidelberg (june 2022)
• rényi-100 - 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)
• lu-nu-umn 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 otto-von-guericke-universität 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, msca-rise 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 urbana-champaign (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); 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 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 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, 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)

• email: lwarnke@ucsd.edu
• address: 比利时vs摩洛哥足彩 , university of california, san diego, 9500 gilman drive #0112, la jolla, ca 92093, us
• office: ap&m 7337