Answer by alvarezpaiva for New grand projects in contemporary math
The simultaneous study of a space $X$ and its observables $F(X)$ (real, complex, or operator-valued functions on $X$) is an old topic, but with quantum groups and non-commutative geometry it has been...
View ArticleAnswer by Ricky for New grand projects in contemporary math
The Langlands program. It goes back to the sixties, but in the last years, with the proof of the fundamental lemma by Ngô Bảo Châu and with several results in the local case, it became one of the most...
View ArticleAnswer by Benoît Kloeckner for New grand projects in contemporary math
Optimal transport. Both its study (generalizations, Monge problem, regularity issues, and geometric properties to cite the part I work in) and its applications (to geometry notably with the Work of...
View ArticleAnswer by Benoît Kloeckner for New grand projects in contemporary math
Ricci flow. It did solve Poincaré's conjecture and the $1/4$-pinching conjecture, but has also become an object of study. More generally, it has launched a large amount of work on geometric flows (mean...
View ArticleAnswer by user30304 for New grand projects in contemporary math
Hyperfields"Krasner, Marshall, Connes and Consani and the author came tohyperfields for different reasons, motivated by different mathematicalproblems, but we came to the same conclusion: the...
View ArticleAnswer by AAK for New grand projects in contemporary math
There is the derived algebraic geometry program of Jacob Lurie, starting with his thesis in 2007 and building on the work of ..., Simpson, Toën-Vezzosi, etc. In the words of Lurie, this is basically...
View ArticleAnswer by Yuichiro Fujiwara for New grand projects in contemporary math
Does compressed sensing count as math? If it does, here is a blog post from the horse's mouth.Edit: For those who would like a popular article, here is a good one in Wired (by JSE if I'm not mistaken)....
View ArticleAnswer by David Corwin for New grand projects in contemporary math
Manjul Bhargava's new field of arithmetic invariant theory is a perfect example of a new grand project. It began with Manjul's doctoral thesis, in which he presented a completely new view of Gauss's...
View ArticleAnswer by user30304 for New grand projects in contemporary math
Tropical mathematicsThe algebraic geometry, analysis and other mathematics over the tropical semiring instead of the real numbers.
View ArticleAnswer by user30304 for New grand projects in contemporary math
Large Networks and Graph Limits - new AMS book by László Lovász"The theory has rich connections with other approaches to the study of large networks, such as ``property testing'' in computer science...
View ArticleNew grand projects in contemporary math
When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which spread into many...
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