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Friday August 18th at 10.15 - 14.00 in room B1036
JACOB LURIE (Harvard):
Elliptic cohomology and derived algebraic geometry, I
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Friday August 25th at 10.15 - 14.00 in room B1036
JACOB LURIE (Harvard):
Elliptic cohomology and derived algebraic geometry, II
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Friday September 1st at 10.15 - 14.00 in room B1036
JACOB LURIE (Harvard):
Elliptic cohomology and derived algebraic geometry, III
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Friday September 22nd at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, I
This is the first and most leisurely of a series of lectures on the theory
and applications of infinity-categories. I will spend most of the time
developing an intuition for the theory of infinity-categories through
examples and elementary constructions. The only prerequisites are some
elementary homotopy theory, a little model category theory, and natural
curiosity.
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Friday September 29th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, II
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Wednesday October 4th at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological Hochschild homology, I
We introduce THH and discuss its structural properties.
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Friday October 6th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, III
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Tuesday October 10th at 14.15 - 16.00 in room B63
JOHN ROGNES:
Topological Hochschild homology, II
We compute the homology and homotopy of THH for finite fields.
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Friday October 13th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, IV
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Wednesday October 18th at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological Hochschild homology, III
We turn to THH of rings of integers.
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Wednesday October 25th at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological Hochschild homology, IV
We relate THH to Kähler differentials and logarithmic poles.
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Wednesday November 1st at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological Hochschild homology, V
We discuss the descent properties of relative THH for local number fields.
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Friday November 10th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, V
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Wednesday November 15th at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological Hochschild homology, VI
We turn to THH of topological K-theory and complex bordism.
Lecture notes can
be found here.
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Friday November 17th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, VI
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Tuesday November 21th at 14.15 - 16.00 in room B63
CLARK BARWICK:
Homotopical algebraic geometry, I
In this lecture, I introduce the basic concepts of homotopical algebraic
geometry; I focus in particular on moduli problems and the geometry of
functors. This will lead us naturally to topos theory. The prerequisites
today will be kept to a bare minimum.
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Wednesday November 22nd at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological André-Quillen (co-)homology, I
Following Basterra, I will introduce the topological André-Quillen
homology TAQ^A(B) of a commutative A-algebra B as the derived version
of the Kähler differentials Omega^1_{B/A}, also known as the
cotangent complex. Following Basterra and Mandell, we will identify
TAQ with the spectrum obtained by iterating (a reduced form of) THH.
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Friday November 24th and Saturday November 25th
Topology meeting in
Trondheim.
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Friday December 1st at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-Categories for Fun and Profit, VII
This lecture represents a change of pace from the previous
lectures. Using the framework of multicategories and Rezk multicategories,
I will begin to discuss the homotopy of algebraic structures and the
vitally important Toën conjectures. These discussions will have a
direct impact on the homotopical algebraic geometry seminar.
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Wednesday December 6th at 12.15 - 14.00 in room B91
JOHN ROGNES:
Topological André-Quillen (co-)homology, II
Following Minasian, we will see that there is a Quillen-type spectral
sequence from the extended powers of TAQ to THH. Turning to calculations,
Basterra and Mandell identify TAQ for spherical group rings, Thom spectra
and HF_p.
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Friday December 8th at 12.15 - 14.00 in room B91
CLARK BARWICK:
Infinity-Categories for Fun and Profit, VIII
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Monday December 11th at 12.15 - 14.00 in room B91
CLARK BARWICK:
Homotopical algebraic geometry, II
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Friday December 15th at 12.15 - 14.00 in room B91
CLARK BARWICK:
Infinity-Categories for Fun and Profit, IX