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 Jirka
 AviFest, AviStories and Amazing Cash Prizes.
 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 More Math from Facebook
 The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.
 The Quantum Computer Puzzle @ Notices of the AMS
 Three Conferences: Joel Spencer, April 2930, Courant; Joel Hass May 2022, Berkeley, Jean Bourgain May 2124, IAS, Princeton
Top Posts & Pages
 Jirka
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 Believing that the Earth is Round When it Matters
 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 AviFest, AviStories and Amazing Cash Prizes.
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Search Results for: erdos
Some old and new problems in combinatorics and geometry
Paul Erdős in Jerusalem, 1933 1993 Update: Here is a link to a draft of a paper* based on the first part of this lecture. Some old and new problems in combinatorial geometry I: Around Borsuk’s problem. I just came back from … Continue reading
New Ramanujan Graphs!
Margulis’ paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis’ paper where the graphs are defined and their girth is studied. (I will come back to the question … Continue reading
Posted in Algebra and Number Theory, Combinatorics, Open problems
Tagged Ramanujan graphs
10 Comments
Happy Birthday Ron Aharoni!
Ron Aharoni, one of Israel’s and the world’s leading combinatorialists celebrated his birthday last month. This is a wonderful opportunity to tell you about a few of the things that Ron did mainly around matching theory. Menger’s theorem for infinite … Continue reading
A Few Mathematical Snapshots from India (ICM2010)
Can you find Assaf in this picture? (Picture: Guy Kindler.) In my post about ICM 2010 and India I hardly mentioned any mathematics. So here are a couple of mathematical snapshots from India. Not so much from the lectures themselves but … Continue reading
Posted in Conferences, Open problems
Tagged Assaf Naor, Eric Rains, François Loeser, Günter Ziegler, ICM2010
1 Comment
The Quantum Debate is Over! (and other Updates)
Quid est noster computationis mundus? Nine months after is started, (much longer than expected,) and after eight posts on GLL, (much more than planned,) and almost a thousand comments of overall good quality, from quite a few participants, my … Continue reading
Some Updates
Jeff Kahn was in town: so we worked together also with Ehud Friedgut and Roy Meshulam (and others) quite intensively. Very nice! Stay tuned for a report! Polynomial Hirsch conjecture (polymath3): While the conjecture remains wide open there are some … Continue reading
Posted in Updates
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Celebrations in BarIlan, HU, and the Technion; A new blog: Windows on Theory; Turing’s celebration on “In Theory”; Graph Limits in Princeton
Last monday we had the annual meeting of the Israeli Mathematical Union (IMU) that took place this year in BarIlan University in Ramat Gan. (IMU is famously also the acronym of the International Mathematical Union but in this post IMU will stand for “Isreali Mathematical Union.”) … Continue reading
Posted in Conferences, Updates
2 Comments
Cap Sets, Sunflowers, and Matrix Multiplication
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Grouptheoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
Discrepancy, The BeckFiala Theorem, and the Answer to “Test Your Intuition (14)”
The Question Suppose that you want to send a message so that it will reach all vertices of the discrete dimensional cube. At each time unit (or round) you can send the message to one vertex. When a vertex gets the … Continue reading
Around Borsuk’s Conjecture 1: Some Problems
Greetings to all! Karol Borsuk conjectured in 1933 that every bounded set in can be covered by sets of smaller diameter. In a previous post I described the counterexample found by Jeff Kahn and me. I will devote a few posts … Continue reading