Bhargav Narayanan
Rutgers University-New Brunswick, NJ·Mathematics & Statistics·Early-career
Many questions in mathematics, computer science and physics come down to the same basic objects: collections of subsets of a finite set, called set-systems. These can be pictured inside the Boolean hypercube, the set of all yes/no strings of a given length.
- Fields
Mathematics & Statistics
Computer Science
- Topics
discrete mathematics
combinatorics
probability
- Grants
- 1 known grant, through Jun 2028
What they work on
- Study up-sets and down-sets in the Boolean hypercube from a probabilistic viewpoint, where they encode events of interest in probabilistic combinatorics and statistical physics.
- Investigate extremal questions about set-systems, including intersecting families in which every two sets share an element, using combinatorial and analytic techniques.
- Examine geometric and topological views of set-systems, treating up-sets and down-sets as discrete half-spaces in convex geometry and as simplicial complexes in topology.
More about the research
Two special kinds, up-sets and down-sets, are especially common. An up-set is a family that stays in the family whenever you add more elements to one of its sets; a down-set is the reverse. Understanding these objects better could support progress across several fields at once.
Why it matters
This is basic mathematics research. A better understanding of up-sets, down-sets and other set-systems could provide new techniques for theoretical computer science, statistical physics and other areas of mathematics, where these objects serve as basic building blocks.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jacob Fox
Stanford University, CA·Mathematics & Statistics
Determine how the number of colors and the structure of hypergraphs, networks whose edges can join more than two points, govern the off-diagonal growth of hypergraph Ramsey numbers.
Huy Pham
California Institute of Technology, CA·Mathematics & Statistics·Early-career
Develop new toolkits for first moment obstructions, where counting expected copies of a structure rules it out, to close gaps in the theory of threshold phenomena in random discrete systems.
Pablo Soberon Bravo
CUNY Bernard M Baruch College, NY·Mathematics & Statistics·Early-career
Show that high-dimensional mass partition problems, such as the Stone-Tukey theorem on cutting several objects into equal halves at once, are deeply connected to fair partition problems such as envy-free division.
The school
Rutgers University-New Brunswick: 57 labs on PI Pages, $837M a year on research, 713 research doctorates a year.
Reach out
A start for your email. Fill in the brackets.