Xavier Pérez Giménez (*) (he/him/his)

Research interests

• Probabilistic methods in combinatorics
• Random structures
• Graph theory
• Asymptotic enumeration
• Discrete probability
• Algorithms

Selected publications

1. Perfect matchings and Hamiltonian cycles in the preferential attachment model (preprint) (doi)
   (with A. Frieze, P. Prałat and B. Reiniger)
   Random Structures & Algorithms, 54(2):258-288, 2019.


2. Arboricity and spanning-tree packing in random graphs (preprint) (doi)
   (with P. Gao and C.M. Sato)
   Random Structures & Algorithms, 52(3):495-535, 2018.


3. Asymptotic enumeration of strongly connected digraphs by vertices and edges (preprint) (doi)
   (with N. Wormald)
   Random Structures & Algorithms, 43(1):80-114, 2013.


4. Disjoint Hamilton cycles in the random geometric graph (preprint) (doi)
   (with T. Müller and N. Wormald)
   Journal of Graph Theory, 68(4):299-322, 2011.


5. On the chromatic number of random d-regular graphs (preprint) (doi)
   (with G. Kemkes and N. Wormald)
   Advances in Mathematics, 223(1):300-328, 2010.

Slides of recent talks

• Perfect matchings in the random bipartite geometric graph. (Based on previous slides by Abigail Raz)
• The chromatic number of a random lift of a regular graph.
• On-line size Ramsey number for monotone k-uniform ordered paths with uniform looseness.
• Perfect matchings and Hamiltonian cycles in the preferential attachment model.
• Strong-majority bootstrap percolation on regular graphs.
• A probabilistic version of the game of zombies and survivors on graphs.
• Arboricity and spanning-tree packing in random graphs with an application to load balancing.
• Asymptotic enumeration of sparse strongly connected digraphs by vertices and edges.
• The chromatic number of random regular graphs.

Workshops organized

• Graduate Research Workshop in Combinatorics. June 2021, online (GRWC 2021)
• AMS Sectional Meeting, SS on "Random Discrete Structures". October 2020, online (program)
• Graduate Research Workshop in Combinatorics. May 2020, Minneapolis MN (cancelled due to Covid-19)
• AMS Sectional Meeting, SS on "Random Discrete Structures". March 2020, Medford MA (cancelled due to Covid-19)
• Graduate Research Workshop in Combinatorics. June 2019, Lawrence KS (GRWC 2019)
• AMS Sectional Meeting, SS on "Random Discrete Structures". March 2019, Auburn AL (program)
• AMS Sectional Meeting, SS on "Random Discrete Structures". April 2018, Nashville TN (program)
• Workshop on "Random Geometric Graphs and Their Applications to Complex Networks". November 2016, Banff (Canada). (BIRS 16w5095)

Students & postdocs

• Abigail Raz (postdoc 2019--21). Now an assistant professor at the Cooper Union
• Alyssa Whittemore (PhD student 2015--2021)
• Leilani Pai (PhD student 2017--Present)
• Austin Eide (PhD student 2017--Present)

Recent teaching

• Math310 - Introduction to Modern Algebra (Spring 2021) - syllabus, class pictures 1 and 2


• Math452 - Graph Theory (Fall 2020) - syllabus
• Math310 - Introduction to Modern Algebra (Fall 2020) - syllabus
• Math852 - Discrete Mathematics II (Spring 2020) - syllabus, class picture
• Math314 - Linear Algebra (Spring 2020) - syllabus, class picture


• Math850 - Discrete Mathematics I (Fall 2019) - syllabus, class picture
• Math487/887 - Probability (Fall 2019) - syllabus, class picture
• Math314 - Linear Algebra (Spring 2019) - syllabus, class picture


• Math958 - Probabilistic Methods in Combinatorics (Fall 2018)
• Math314 - Linear Algebra (Fall 2018)
• Math852 - Discrete Mathematics II (Spring 2018)


• Math850 - Discrete Mathematics I (Fall 2017)
• Math208 - Calculus III (Fall 2017)
• Math 221 - Differential Equations (Spring 2017)


• Math 221 - Differential Equations (Fall 2016)
• Math 221H - Honors Differential Equations (Fall 2016)

Other stuff i like

• Outdoors: this, this, that...
• Swing dancing with Sarah
• Holding my twins night and day