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900_Changelog

Todos

MOCs 4

Projects 24

Quick_Notes 100

Seminars and Talks 3

To Review 50

Unsorted

2-category

2021-04-23 Advice on research and problems

A hat genus

A1 Homotopy

ADE singularities

AKLB setup

A_infty

Aatiyah-Singer Index Theorem

Adeles

Alexander duality

Algebraic Topology

Algebraic Variety

Analysis MOC

Andrew Blumberg, Floer homotopy theory and Morava K-theory

Arakelov

Arpon Raksit - Hochschild homology and the derived de Rham complex revisited

Arthur's conjecture

Artin approximation

Artin map

Artin stack

Artin symbol

Artin-Rees theorem

Artin-Schreier

Artinian category

Atiyah Hirzebruch spectral sequence

BGG resolution

BV algebra

B_dr

Balmer spectrum

Barr-Beck

Berkovich spaces

Betti moduli

Beuzart-Plessis, On the spectral decomposition of the Jacquet-Rallis trace formula and the Gan-Gross-Prasad conjecture for unitary groups

Birch and Swinnerton-Dyer conjecture

Blakers Massey

Blakers Massey theorem

Bloch-Kato

Bockstein

Bordism spectra

Borel

Borel regulator

Bott Periodicity

Bousfield localization

Brauer group

Bredon cohomology

Brill-Noether theorem

Brown-Peterson spectra

BunG

Burnside ring (algebraic geometry)

Course

CM field

CW approximation

CW complex

CY metric

Calabi-Yau

Calabi-Yau manifold

Calabi-Yau object of a category

Cartesian closed category

Cartier divisor

Cauchy completion

Cayley-Hamilon theorem for modules

Cech cohomology

Chebotarev density

Chern class

Chern-Ruan theory

Chern-Simons

Chern-Simons invariant

Chevalley-Eilenberg complex

Chow ring

Classical homological algebra

Clifford algebra

Cohen-Lenstra

Cohomology of BSO

Cohomology of loop spaces of spheres

Contact

Contact project

D modules

DG category

DGA

DVR

Day convolution

Dedekind domain

Dedekind zeta function

Dedekind-Kummer theorem

Deformation space

Dehn invariant

Deligne-Mumford stack

Dieudonne module

differential geometry

Dirac equation

Dirichlet's theorem

Dirichlet's unit theorem

Dolbeaut cohomology

Dold-Kan correspondence

EHP sequence

E_n ring spectrum

Eilenberg-MacLane spaces

Einstein equations

Eisenstein polynomial

Eisenstein series

Elliptic cohomology

Enriques surface

Enriques-Kodaira Classification

Euler class

Euler exact sequence

Euler sequence

Exercises in complex AG

Faltings theorem

Fano variety

Fermat quartic

Fermat's Last Theorem

Finset

Floer Theory

Floer homotopy

Formal group

Fredholm operator

Freudenthal suspension

Frobenius morphism

Frobenius twist

Fukaya category

Fundamental SESs in commutative algebra

GAGA

GIT quotient

GRH

Galois cohomology

Galois correspondence

Galois descent

Galois representations

Galois theory

Gamma function

Gauss' lemma

Gauss-Manin

Gelfand duality

Gelfand representation

General relativity

Generalized Poincare Conjecture

Geometric Topology (Subject MOC)

Geometrization

Gerstenhaber bracket

Giroux correspondence

Goodwillie calculus

Gorenstein

Grassmannian

Gromov-Witten invariants

Grothendieck category

Grothendieck-Lefschetz Trace Formula

Gysin sequence

H-space

HKR

HOTT

Haar measure

Hamiltonian

Hard Lefschetz

Semester One

Hasse bound

Hasse bounds

Hasse invariant

Hasse principle

Hasse-Weil L function

Hasse-Weil Zeta

Heegard-Floer homology

Hensel's Lemma

Hermitian

Higgs bundle

Hilbert 12

Hilbert 90

Hilbert Basis Theorem

Hilbert class field

Hilbert scheme

Hilbert symbol

Hirzebruch-Riemann-Roch

Hodge F-crystal

Hodge decomposition

Hodge diamonds

Hodge filtration

Hodge index theorem

Hodge polygon

Hodge star

Hodge theory

Hodge-Tate conjecture

Hodge-Tate theory

Hodge-to-deRham degeneration

Holonomy Classification

Homological Algebra Talk

Homological Stability Course Notes

Homotopy of schemes

Hopf algebra

Hopf fibration

Hopf invariant one

Hurewicz

Hurwitz space

Hurwitz theorem

Ideles

Ind construction

Ind objects

Motivation

Integration along the fiber

Introduction to infinity categories

J-homomorphism

Jacobi theta

Jacobian

K-Theory

K3 surface

K3 Surfaces

Kahler

Kahler problem

Kan complex

Kan extension

Kazhdan Lusztig conjecture

Kervaire invariant one

Killing form

Topics

Kodaira Dimension

Kodaira vanishing

Kodaira-Spencer

Kronecker symbol

Kronecker-Webber theorem

Krull dimension

Krull's intersection theorem

Krull's principal ideal theorem

Krull's theorem

Kummer sequence

Kummer theory

Kuranishi charts

L function

L infty algebra

Lagrangian

Lagrangian Floer homology

Landweber exactness

Langlands

Laplace-Beltrami operator

Lazard ring

Learning Goals 2021

Learning Resources: Algebraic Topology

Learning Resources: Number Theory

Learning Resources: Symplectic Topology/Geometry

Lefschetz fixed point theorem

Lefschetz hyperplane theorem

Lefschetz motive

Leray spectral sequence

Lie algeberoid

Lie algebra

Lie algebra types

Lie algebra valued form

Lie algebroid

Lie group

Liouville manifold

Liouville vector field

Log geometry

Lubin-Tate theory

Luna etale slice theorem

Mackey functor

Manifolds Definitions

Mapping cylinder

Maschke's theorem

Masterclass in Condensed Mathematics

Math Reading List

Maurer-Cartan

May recognition principle

Mazur Program B

Milnor Conjecture

Minkowski bound

Mock AMS 2020 Pictures

Model category theory

Moore spaces

Moore spectrum

Morava E theory

Morava K theory

Mordell-Weil

Mordell-Weil rank

Morita equivalence

Morse Theory

Morse lemma

Nakayama's lemma

Neron Severi

Neron-Tate height

Nishida's Theorem

Nisnevich topology

Noether Normalization

Noetherian

Normalization

Notes - The cotangent complex and derived de Rham cohomology

Novikov ring

Number theory

Nygaard filtration

O(D) for D a divisor

O_X module

Open Problems

PBW basis

Paper Reading List

Papers to Read

Pell equation

Physics

Picard group

Pin group

Plucker embedding

Generalized Topological Poincaré Conjecture

Poincare bundle

Poincare homology sphere

Poincare series

Poisson structure

Poisson summation

Pontrayagin class

Pontrayagin-Thom

Pontryagin dual

Postnikov tower

Principal series representations

Prismatic Cohomology Notes

Project Ideas

Project Queue

Projects

Quantum Homology Theories

Quick Notes

Quillen K Theory

Quillen adjunction

Quillen equivalence

RAPC

Ramanujan-Petersson conjecture

Reading Group_Fargues Fontaine Curve

Reading notes - Singular Points on Complex Hypersurfaces

Rees construction

representation theory

Representing cohomology

Ricci curvature

Ricci flow

Ricci-flat

Riemann Hypothesis

Riemann Zeta

Riemann zeta function

Riemann-Hilbert correspondence

Riemann-Roch

Riemannian curvature

Riemannian geometry

Rohklin's theorem

Rokhlin theorem

SH

SL2

SYZ torus fibration

Sard-Smale

Sato-Tate conjecture

Schoenflies conjecture

Schur's Lemma

Schwartz space

Segal spaces

Seiberg-Witten theory

Selmer group

Serre class

Serre duality

Serre fibration

Serre spectral sequence

Serre's conjecture on vector bundles

Serre-Swan

Serre-Tate theory

Shimura variety

Shimura-Taniyama-Weil

Siegel modular forms

Skolem-Noether theorem

Spanier-Whitehead duality

Stable Homotopy Seminar

The Adams Spectral Sequence

Steenrod algebra

Stein

Stephen Hawking

Stiefel manifold

Stiefel-Whitney class

Stieltjes integral

Stokes theorem

Stone-Cech compactification

Strong approximation

Subjects 1

Superstring theory

THH

TQFT

Talbot Talk 1

Talbot Talk 2

Talks

Tamagawa numbers

Tannakian

Tate module

Tate-Shafarevich group

Thom form

Thom space

Three Things Exercise

Three-manifolds MOC

Topological cyclic homology

Torelli

Tsen's theorem

Twisted K theory

Universal family

VHS

Archimedean place

Vandiver's conjecture

Videos

Waldhausen S construction

Weak approximation

Weierstrass p function

Weil Conjectures

Weil cohomology

Weil divisor

Weil reciprocity

Weinstein

Weyl group

When are spheres Lie groups

Whitehead's theorem

Whitehead torsion

Whiteney embedding theorem

Whitney trick

Why study K theory

Witt's lemma

Yang-Mills

Yoneda lemma

Zariski Descent

Zariski tangent space

Zariski's lemma

Zariski's main theorem

Zariski's theorem

Zhiwei Yun project group

a stack is a category fibered in groupoids

abelian category

abelian variety

absolute Galois group

absolute value

accidental isomorphisms

adelic group

adic completion

adjoint

adjoint representation

adjunction formula

admissible representation

advice on talks

algebra over a ring

algebraic curve

Algebraic de Rham cohomology

algebraic group

algebraic space

almost complex structure

alpha invariant

alteration

ample

ample divisor

analytic class number formula

animated rings

anti self dual

antiholomorphic involution

arithmetic Frobenius

arithmetic and 3-manifolds

arithmetic genus

arithmetic geometry

arithmetic progressions

aspherical space

assembly

associahedra

associated bundle

automorphic L function

automorphic form

automorphic representation

bar construction

base change

basic tools in homotopy of spaces

Topics

belong

bicategory

big

rational morphism

birational

bisimplicial set

blowup

bordered Heegaard Floer homology

canonical bundle

canonical divisor

cartesian fibration

categorification

cellular approximation

cellular map

central fiber

central simple algebra

character variety

characteristic class

characters

chromatic homotopy theory

class field theory

classical category theory

classifying space

closed immersion

clutching function

coalgebra

coarse moduli space

cobordism

cobordism hypothesis

cobordism spectrum

cocompact

cocone

coend

coequalizer

cofiber sequence

cofinal functor

cogroup

coherent module

coherent sheaves

cohomological criterion for ampleness

cohomological dimension

cohomological field theory

cohomology of unitary groups

cohomology operations

cohomology rings as coalgebras

cohomology theory

cohomolology theory

cohomotopy

coinvariants

colimit

compact object of a category

compact-open topology

compactly generated space

complete

complex bordism

complex oriented cohomology theory

condensed set

conductor

cone category

configuration space

congruence subgroup

connected ring

connection

connectivitty

conormal exact sequence

conormal sequence

conservative functor

constructible sheaf

constructing BU_n

continuous group cohomology

contraction

coproduct

correspondences

cosheaf

cosmos

cotangent complex

covariant derivative

covering

covering space

covolume

crepant

crystalline Frobenius

crystalline cohomology

crystalline conjecture

curvature

curvature form

curves

cusp form

cyclotomic character

de Rham conjecture

de Rham isomorphism

de Rham moduli

de Rham-Witt cohomology

deformation

deformation quantization

deformation theory

deformation theory is controlled by dg Lie algebras

deformation to the normal cone

degeneration

degree of a closed point

degree of a morphism

delta function

density

depth

derivation

derived algebraic geometry

derived category

derived de Rham cohomology

derived lci

derived ring

derived scheme

derived stacks

descent

descent category

devissage

dg Lie algebras

dg manifold

diagonal morphism

different

differential forms

dimension

dimension shifting

direct image

discrete log problem

discriminant

distributions

divisor

divisor class group

dominant morphism

dualizable objects in a category

dualizable object of a category

dualizing sheaf

effective descent

elliptic complex

elliptic curve over a scheme

elliptic operator

For curves

endomorpism algebras

enriched category

equivalence of categories

equivariant

equivariant K theory

equivariant cochains

equivariant cohomology

equivariant functor

equivariant homotopy theory

equivariant stable homotopy theory

ergodic

etale

exact triangle

examples of cohomology rings

examples of computations of etale cohomology

examples of spectral sequences

excellent ring

factorial

factorization algebra

factorization homology

faithful functor

faithfully flat

families

fiber product

fibrant and cofibrant objects

fibration

field norm

filtered spectra

fine moduli space

fine sheaf

finite spectrum

finite type

finitely presented

flag variety

flat bundle

flat connection

flow

flow categories

foliate

formal disk

formal spectrum

formally etale

formally smooth

formally unramified

4-manifolds

fourier transform

fractional ideal

frame bundle

frames

framed bordism

free cocompletion

function field

functor of points

fundamental class

fundamental group

fundamental unit

galois morphism

gauge theory

geodesics

geometric Langlands

geometric fiber

geometric realization

gerbe

gimbal lock

Global field

The Going Down Theorem

going up theorem

good reduction

group actions on categories

group algebra

group cohomology

group object

group scheme

groupoid

h-cobordism

handle decomposition

height

herbrand quotient

higher category

higher classifying spaces for topological groups

highest weight

holonomy

holonomy group

homogeneous space

homological mirror symmetry

homological stability

homology of a point as a coefficient ring

homology sphere

homotopy

homotopy category

homotopy coherence

homotopy equivalent manifolds are cobordant

homotopy fiber

homotopy fixed points

homotopy groups

homotopy groups of spheres

homotopy sum

homotopy theory

homotopy type

hyper-descent

hyperbolic 3-manifold

hypercohomology

hypercovering

hyperellptic

ideal class group

ideal correspondence for localizations

ideal sheaf

idemptotent-complete category

index of a Morse function

induction

infinity categories

infinity groupoids

integrally closed

internal category

intersection form

intersection theory

invariant theory

inverse Galois problem

invertible module

invertible object of a category

invertible sheaves

irreducible divisor

j invariant

kahler identities

koszul duality

l-adic cohomology

l-adic representations

lambda connection

lax

lax functor

lefschetz pencil

left invariant vector field

level structure

limit

line bundle

linear category

linearly equivalent divisors

list of K theory rings

examples of fibrations

local complete intersection

local on the base

local spectra

local system

local theta correspondence

local to global

localization (category theory)

localization

locally free sheaf

locally quasi-finite

log differential forms

loop space

lying over theorem

manifold with corners

mapping class group

mapping cone

math_quotes

maximal unramified extension

metric

metric tensor

minimal model program

mirror quintic

Mirror Symmetry

mixed characteristic

mixed motive

mixed motives

model of a scheme

modern category theory

modular curve

modular form

modules are like sheaves

modules over a category

modules over an algebra

moduli of formal group laws

moduli stack of elliptic curves

moment map

monad

monodromy representation

monoid

monoid object

monoidal category

monomorphism

motivation for spectral sequences

motive

motivic L function

motivic cohomology

motivic homotopy

multiplicative spectral sequence

nearby cycles

nef divisor

nerve

nilpotent completion

nilpotent thickening

nodal curve

nonabelian Hodge correspondence

nonabelian Poincare duality

nonabelian derived functor

nonarchimedean

norm group

norm map

normal bundle

normal field extension

number field

number field function field analogy

Obstruction Theory

obstruction-deformation theory

open book decomposition

open immersion of schemes

operad

orbifold

orbifold fundamental group

order

orientable

orthogonal group

p-adic Hodge theory

p-adic formal schemes

p-adic integers

p-adic zeta function

parahoric

parallelizable spheres

perfect complexes

perfect field

perfect ring

perfectoid

period

Motivation

periodic sphere spectrum

perverse sheaf

perverse t-structure

pointed category

potentially semistable

potentially semistable conjecture

pregeometry

presentable category

primary

prime avoidance lemma

prime ideal

principal bundle

principal divisor

prismatic cohomology

profinite completion

profinite group

profinite integers

projective

projective object

proper morphism

properties of morphisms

pseudofunctor

pseudoholomorphic curve

pure motive

purity theorem

pushforward

Examples

q series

quadratic form

quadratic reciprocity

quaiseparated

quantization

quantum cohomology

quasicategory

quasicoherent sheaf

quasicompact

quaternion algebra

quotient stack

ramification divisor

ramification index

rational points

ray class field

reciprocity conjecture

reduced

reduced cohomology

reduction mod p

reduction of structure group

reflexive pair

regular ring

regular scheme

Regulator of a number field

relative dimension

relative spec

representation ring

resolution of singularities

riemannian manifold

rigid category

rigid geometry

rigidity

ring of integers

ring spectra

roots of unity

s-cobordism

scalar curvature

scheme

schemes are functors

section conjecture

semilinear action

semilocal ring

semisimple algebra

semistable

semistable conjecture

semistable degeneration

semistable reduction

separable

separable extension

separably generated

separated

sheaf

sheaf cohomology

shifted symmetric functions

signature

simple normal crossings

simple objects of a category

simplicial algebra

simplicial category

simplicial set

site

six functor formalism

skeleta

smash product

smooth algebra

smooth points

smooth scheme

smooth structure

smooth structures

solid mathematics

songruence subgroups

spacetime

span

spec Z as a curve

special fiber

spectra

spectra are modules over the sphere spectrum

spectral category

spectral sequence

spectral sequence of a double complex

spectral sequence of a tower

sphere and disc objects in chain complexes

spherical manifold

spin

splitting principle

sporadic point

stable homotopy

stable homotopy groups of spheres

stable infinity category

stable map

stackification

stacks MOC

stratified

strict normal crossings divisor

stringy topology

structure group

structure sheaf

structured ring spectrum

subcanonical

superalgebra

surface bundle

surgery

symbol

symmetric monoidal infty category

symmetric space

symmetric spectra

symplectic

symplectic group

symplectic quotient

syntomic

tamely ramified

tangent bundle

tate conjecture

tate duality

tautological bundle

tempered

tensor category

tensored

thick subcategory

tilting

topological K theory

topological category

topological stack

topos

tor amplitude

toric geometry

toric varieties

torsion of a connection

torsor

trace (monoidal categories)

trace map

trace pairing

transfers

triangulated categories

triangulated category

tropical geometry

twist

twisted arrow category

twisted cubic

twisting sheaves

uniformization

unit group

unitary trick

universal coefficient theorem

universal enveloping algebra

universally closed

unramified

unramified morphism

unstable homotopy groups of spheres

valuation ring

valuative criterion of properness

valuative criterion of separatedness

vanishing cycles

vector bundles

vertex algebra

vertical and horizontal subspace

very ample divisor

virtual fundamental class

vortex equation

wall-crossing

weak and hard Lefschetz theorems

weak equivalence

weak homotopy equivalence

weighted colimit

weighted projective space

whiskering

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crepant

A map is crepant if the pullback of the canonical divisor is the canonical divisor

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What is a crepant map?

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