University of Haifa – החוג למתמטיקה, אוניברסיטת חיפה
Let us start with two very believable observations: 1. The only functors from the category of all sets to that of finite sets are the constant ones.2. Groups have no natural abelian subgroups.We raise questions about infinite categorical and space…
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The energy spectrum of the hydrogen atom is one of the oldest computations in quantum mechanics, yet in the usual model the Schrodinger operator is singular, non-canonical, and relies on unmotivated boundary conditions. In joint work with Joseph Bernstein, we…
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Invariant metrics appear in most branches of mathematics. Examples include word metrics (entropy, fragmentation) and non-discrete metrics (Hofer norm and Lp) in symplectic, differential geometries and dynamics. In group theory examples include commutator length and primitive length. After providing some…
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We shall describe the quest to classify uncountable linear orders, along the way debunking the claim that “Every nontrivial statement of infinite combinatorics is independent of the axioms of set theory”.This is joint work with Tanmay Inamdar.
The energy spectrum of the hydrogen atom is one of the oldest computations in quantum mechanics, yet in the usual model the Schr¨odinger operator is singular, non-canonical, and relies on unmotivated boundary conditions. In joint work with Joseph Bernstein, we…
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The “Magic Wand” theorem of Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi is a far reaching result regarding the dynamics of an action of the group SL(2, R) on the moduli space of translation surfaces. Its proof (in 2013) was the culmination of many…
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The homotopy groups of CW complexes and of the mapping spaces between them are notoriously difficult to compute. However, if one disregards torsion, rational homotopy theory is very effective and can easily solve such problems. Moreover, it produces efficient invariants…
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Schur-Weyl duality is a cornerstone of representation theory. It has a modern analogue, where modules over the quantum affine algebras (objects of intense study in mathematical physics) are placed in correspondence with modules over affine Hecke algebras, and ultimately, with…
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In 1990, V. Drinfeld introduced the Grothendieck-Teichm¨uller group GT. This group receives the homomorphism from the absolute Galois group GQ of rational numbers and this homomorphism is injective due to Belyi’s theorem. Many challenging questions about GT are motivated by…
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A fundamental class of problems in algebraic topology are the realization problems: when is a given algebraic object realizable as an algebraic invariant of a space? For example, one might ask when a module over the Steenrod algebra arises as…
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