James Cummings is a math professor at Carnegie Mellon University.
Ph.D.: Cambridge University

Personal website


Recent and upcoming talks by James Cummings

James Cummings: Universal graphs

Mathematical logic seminar – Jan 24 2017 Time:     3:30pm – 4:30 pm Room:     Wean Hall 8220 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Universal graphs Abstract: The well-known “random countable graph” or “Rado graph” is a countable graph which contains induced copies of every countable graph. continue reading…

MAMLS at VCU, April 1-2, 2017

MAMLS at VCU will be a gathering of set theorists working on large cardinals, inner models, forcing and relative consistency results, sponsored by the NSF and the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. continue reading…

James Cummings: Cardinal invariants of the continuum

Mathematical logic seminar – October 18 2016 Time:     3:30pm – 4:30 pm Room:     Wean Hall 8220 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Cardinal invariants of the continuum Abstract: The cardinal invariants of the continuum are cardinals which measure properties of the continuum more subtle than its cardinality. continue reading…

Set Theory and its Applications in Topology, September 11-16, 2016

The meeting took place in Oaxaca, Mexico. The slides may be found below. 08:45 – 09:00 Introduction and Welcome (Conference Room San Felipe) 09:00 – 10:00 Alan Dow: The even numbered problems (Conference Room San Felipe) 10:00 – 10:30 Rodrigo Jesus Hernandez Gutierrez: Spaces discretely generated at infinity (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Isván Juhász: Lindelöf spaces of countable pseudocharacter (Conference Room San Felipe) 11:30 – 12:00 Juris Steprans: PID and universal graphs (Conference Room San Felipe) 13:20 – 13:30 Group Photo (Hotel Hacienda Los Laureles) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Itay Neeman: Forcing one instance of the Moore-Todorcevic principle (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 James Cummings: Dowker and super-Dowker filters (Conference Room San Felipe) 17:00 – 17:30 Assaf Rinot: The $\omega_2$-Souslin problem (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Tuesday, September 13 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 10:00 Christina Brech: Bases of Homogeneous families bellow the first Mahlo cardinal (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Piotr Koszmider: A non-commutative Mrówka’s $\Psi$-space (Conference Room San Felipe) 11:30 – 12:00 Asger Tornquist: Invariant descriptive set theory and almost disjointness modulo an ideal (Conference Room San Felipe) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Alexander Shibakov: Sequential groups: large and small (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 Jindrich Zapletal: Strong measure zero sets in Polish groups (Conference Room San Felipe) 17:00 – 17:30 Marcin Sabok: On hyperfiniteness of boundary actions of hyperbolic groups (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Wednesday, September 14 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 09:30 Joerg Brendle: Q (Conference Room San Felipe) 09:30 – 10:00 Dilip Raghavan: More on the density zero ideal (Conference Room San Felipe) 10:00 – 10:30 Osvaldo Guzmán: Combinatorial properties of MAD families (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Victor Torres-Perez: Constructions with oppositions: Cardinal invariants and games (Conference Room San Felipe) 11:30 – 12:00 David Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem (Conference Room San Felipe) 12:00 – 12:30 Natasha Dobrinen: Topological Ramsey spaces in some creature forcings (Conference Room San Felipe) 12:30 – 13:30 Lunch (Restaurant Hotel Hacienda Los Laureles) 13:30 – 17:30 Free Afternoon (Oaxaca) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Thursday, September 15 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 10:00 Slawomir Solecki: Monoid actions on left-topological compact semigroups (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Aleksandra Kwiatkowska: The Ramsey degree of the pre-pseudoarc (Conference Room San Felipe) 11:30 – 12:00 Dana Bartosova: Ultrafilter combinatorics in topological dynamics (Conference Room San Felipe) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Jan van Mill: Erdős spaces (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 Anush Tserunyan: Topological dimension and Baire category (Conference Room San Felipe) 17:00 – 17:30 Yinhe Peng: Weak network and the basis problem (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles) Friday, September 16 07:30 – 09:00 Breakfast (Restaurant at your assigned hotel) 09:00 – 09:30 Jeffrey Bergfalk: Walks… (Conference Room San Felipe) 09:30 – 10:00 Iian Smythe: A local Ramsey theory for block sequences (Conference Room San Felipe) 10:00 – 10:30 Noé de Rancourt: Ramsey theory with and without the pigeonhole principle (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Claribet Piña: Topological partition relations for $\omega^2$ (Conference Room San Felipe) 11:30 – 12:00 Carlos Uzcategui: Bases and selectors for cofinal families of countable sets (Conference Room San Felipe) 12:00 – 12:30 Carlos Di Prisco: Graphs on the Cantor set (Conference Room San Felipe) 12:30 – 14:30 Lunch (Restaurant Hotel Hacienda Los Laureles)   continue reading…

James Cummings: Dowker filters

Seminar will generally be meeting at 3:30pm in Wean Hall 8220 this semester. Please contact me if you would like to speak or to suggest a speaker. Mathematical logic seminar – September 6 2016 Time:     3:30pm – 4:30 pm  (PLEASE NOTE CHANGED TIME FROM LAST YEAR) Room:     Wean Hall 8220 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Dowker filters Abstract: Dowker filters are a class of filters introduced by Dowker in connection with a problem in topology. continue reading…

2016 Graduate summer school in set theory, Irvine, July 25 – August 5 2016

A graduate summer school in set theory will be held July 25 – August 5 2016 at the University of California Irvine. The subject of the summer school will be singular cardinal combinatorics, with a focus on PCF theory. continue reading…

James Cummings: Proper forcing, side conditions and Baumgartner’s problem II

Mathematical logic seminar – March 22 2016 Time:     12:30 – 13:30 Room:     Wean Hall 8220 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Proper forcing, side conditions and Baumgartner’s problem II Abstract: I will continue to talk about proper forcing and Baumgartner’s problem. continue reading…

James Cummings: Proper forcing, side conditions and Baumgartner’s problem

Mathematical logic seminar – February 9 2016 Time:     12:30 – 13:30Room:     Wean Hall 8220 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Proper forcing, side conditions and Baumgartner’s problem Abstract: I will discuss the method of “proper forcing”, some tricks for building proper forcing posets, and applications old and new. continue reading…

Menachem Magidor 70th Birthday Conference, Jerusalem, February 17-19 2016

Menachem Magidor 70th Birthday Conference The Hebrew University of Jerusalem, February 17-19 2016 Reigstration is now open! Invited speakers: Artur Apter (CUNY) Joan Bagaria (ICREA & UB) James Cummings (CMU) Mirna Dzamonja (UEA) Ilijas Farah (York) Matthew Foreman (UCI) Moti Gitik (TAU) Juliette Kennedy (Helsinki) Peter Koepke (Bonn) Jean Larson (UFL) Bill Mitchell (UFL) Ralf Schindler (Münster) Saharon Shelah (HUJI) Dima Sinapova (UIC) John Steel (Berkeley) Jouko Väänänen (Helsinki & ILLC) Boban Velickovic (Paris 7) Matteo Viale (Torino) Philip Welch (Bristol) Hugh Woodin (Harvard) Organizers: Laura Fontanella Itay Kaplan Asaf Karagila Assaf Rinot continue reading…

James Cummings: Forcing Pi_2 statements II

Mathematical logic seminar – September 22, 2015 Time:     12:30 – 13:30 Room:     Wean Hall 7201 Speaker:         James Cummings Department of Mathematical Sciences CMU Title:     Forcing Pi_2 statements II Abstract: We often find ourselves needing to force assertions of the general form “for every x there exists y….” where typically x and y are subsets of some regular cardinal κ We will consider three general cases (of increasing difficulty) κ is ω1 κ is the successor of an uncountable regular cardinal κ is the successor of a singular cardinal continue reading…