Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
To post a seminar which takes place at the Mathematics department, please email seminars@math.harvard.edu with date, time, room, title and possibly with an abstract.
CMSA SPECIAL LECTURE SERIES:TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019: Artan Sheshmani
CMSA
On Derived Algebraic/Differential Geometry
on Tuesday, February 05, 2019, at 3:00 - 4:30 pm in CMSA Building, 20 Garden St, G10
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry/

CMSA SPECIAL LECTURE SERIES:TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019: Artan Sheshmani
CMSA
On Derived Algebraic/Differential Geometry
on Thursday, February 07, 2019, at 3:00 - 4:30 pm in CMSA Building, 20 Garden St, G10
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry/

CMSA SPECIAL LECTURE SERIES: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019: Artan Sheshmani
CMSA
On Derived Algebraic/Differential Geometry
on Tuesday, February 12, 2019, at 3:00 - 4:30 pm in CMSA Building, 20 Garden St, G10
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry/

CMSA SPECIAL LECTURE SERIES: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019: Artan Sheshmani
CMSA
On Derived Algebraic/Differential Geometry
on Saturday, December 14, 2019, at 3:00 - 4:30 pm in CMSA Building, 20 Garden St, G10
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry/

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