# Simons Collaboration on Homological Mirror Symmetry

The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving **Homological Mirro****r Symmetry (HMS)** in full generality, and fully exploring its applications.

**Mirror symmetry**, which emerged in the late 1980s as an unexpected physical duality between quantum field theories, has been a major source of progress in mathematics. At the 1994 ICM, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model).

We envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints:

- categorical algebraic geometry and
**non-commutative (nc) spaces**: in this language, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry. - the
**Strominger-Yau-Zaslow (SYZ)**approach, which provides a global geometric prescription for the construction of mirror pairs. - Lagrangian Floer theory and
**family Floer cohomology**, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.

**The Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester:**

**Jacob Bourjaily**(*Neils Bohr Institute*) 4/1/2018 – 4/14/2018**Colin Diemer**(*IHES)*2/25/2018 – 3/10/2018**Baohua Fu**(*Chinese Academy of Sciences*) 4/15/2018 – 4/28/2018**Andrew Harder**(*University of Miami*) 4/15/2018 – 4/28/2018**Shinobu Hosono**(*Gakushuin University*) 2/25/2018 – 3/10/2018**Adam Jacob**(*UC Davis*) 3/5/2018/ – 3/16/2018**Ivan Loseu**(*Northeastern University*) 1/21/2018 – 2/3/2018**Cheuk-Yu Mak**(*Cambridge University*) 4/1/2018 – 4/15/2018**Daniel Pomerleano**(*Imperial College*) 3/19/2018 – 3/23/2018**Mauricio Romo**(*Tsinghua University*) 4/1/2018 – 4/18/ 2018**Emanuel Scheidegger**(*Albert Ludwigs University of Freiburg*) 2/22/2018 – 3/22/2018**Dmytro Shklyarov**(*Technische Universität Chemnitz*) 3/4/2018 – 3/17/2018**Matt Young**(*Chinese University of Hong Kong*) 1/15/2018 – 2/9/2018**Jeng-Daw Yu**(*National Taiwan University*) 4/2/2018 – 4/6/2018**Minxian Zhu**(*Yau Mathematical Sciences Center, Tsinghua University*) 1/ 22/2018 – 2/25/2018

The Center will also be hosting a four-day** Simons Collaboration Workshop on Homological Mirror Symmetry and Hodge Theory **on January 10-13, 2018, and another April 5-7. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. **Click here for more information.**