site address: decusinlabore.wordpress.com redirected to: decusinlabore.wordpress.com

site title: Decus in Labore

Our opinion (on Thursday 27 August 2026 23:38:57 UTC):

- no comments

Meta tags:

Headings (most frequently used words):

and, in, the, decus, labore, menu, quantum, ergodicity, large, deviations, cramer, theorem, entropy, set, projections, root, systems, torsion, on, jacobians, teichmuller, dynamics, semisimplicity, of, kontsevich, zorich, cocycle, grothendieck, generalized, hodge, conjecture, functions, nice, each, variable, separately, descent, for, vector, spaces, holomorphic, bundles, with, hyperbolic, fibers, post, navigation, recent, posts, archives, blogroll, follow, blog, via, email,

Text of the page (most frequently used words):
the (74), and (27), this (21), for (13), comment (11), some (11), posted (10), tagged (10), simion (10), continue (10), reading (10), that (10), will (10), with (9), theorem (9), post (9), leave (9), theory (9), dynamics (8), have (7), 2013 (7), teichmuller (7), below (7), proof (7), hodge (7), decus (6), labore (6), 2014 (6), systems (6), entropy (6), projections (6), large (6), holomorphic (6), following (6), how (6), each (6), wordpress (5), email (5), january (5), deviations (5), hyperbolic (5), flat (5), complex (5), example (5), are (5), about (5), result (5), like (4), com (4), follow (4), torsion (4), jacobians (4), set (4), kobayashi (4), fibration (4), not (4), manifold (4), then (4), paper (4), real (4), fold (4), more (4), variable (4), separately (4), analytic (4), ergodic (4), dynamical (4), these (4), random (4), zorich (4), different (4), inequality (4), blog (3), posts (3), geometry (3), july (3), september (3), root (3), cramer (3), quantum (3), ergodicity (3), rigidity (3), bundles (3), locally (3), unit (3), holomorphically (3), one (3), suppose (3), note (3), available (3), here (3), would (3), record (3), algebraic (3), from (3), notes (3), analysis (3), but (3), continuous (3), consider (3), nice (3), conjecture (3), grothendieck (3), surfaces (3), discuss (3), ideas (3), semisimplicity (3), namely (3), definitions (3), properties (3), variables (3), two (3), appears (3), let (3), probability (3), site (2), required (2), content (2), log (2), sign (2), subscribed (2), subscribe (2), now (2), address (2), new (2), via (2), what (2), 2012 (2), april (2), october (2), 2015 (2), february (2), 2016 (2), manifolds (2), trivial (2), can (2), see (2), must (2), brief (2), says (2), into (2), proved (2), algebra (2), galois (2), mainly (2), own (2), benefit (2), version (2), results (2), type (2), prove (2), even (2), cauchy (2), should (2), measurable (2), functions (2), wrote (2), general (2), try (2), explain (2), bit (2), concepts (2), aspects (2), familiarity (2), assumed (2), survey (2), kontsevich (2), cocycle (2), describe (2), bourbaki (2), their (2), there (2), main (2), planes (2), dimensions (2), exponentially (2), simple (2), fast (2), flow (2), density (2), microlocal (2), eigenfunctions (2), laplacian (2), get, started, design, website, name, write, loading, comments, collapse, bar, manage, subscriptions, view, reader, report, privacy, already, account, theme, publish, konstantin, kovshenin, proudly, powered, enter, your, receive, notifications, terry, tao, imagination, disquisitiones, mathematicae, blogroll, november, december, archives, recent, search, older, navigation, requirement, means, isomorphic, ball, natural, projection, disk, using, maximum, principle, details, remark, fiber, gluing, maps, overlapping, local, charts, constant, was, inspired, definition, informally, map, arbitrarily, disks, certain, sense, most, royden, mathoverflow, fibers, linear, basic, things, descend, data, along, extensions, fields, benefited, conrad, online, exposition, shorter, those, descent, vector, spaces, state, them, hartogs, contrast, situation, defining, function, origin, classical, question, need, both, although, incorrectly, said, obvious, famously, called, observations, made, false, reasons, generalized, variations, structures, connect, leads, various, applications, implies, invariant, also, mention, multiplication, factors, arises, contains, number, somewhat, disparate, methods, walks, homogeneous, smooth, interact, essential, explained, anton, special, case, points, which, curves, zeroes, form, land, factor, jacobian, moeller, reduced, reference, lie, groups, algebras, proofs, just, summary, consists, lists, application, involving, whose, generalizations, much, conceptual, denotes, taking, indicators, bound, follows, however, proving, requires, work, above, mixed, schwartz, holder, inequalities, generalizes, sets, higher, subspaces, possibly, long, coordinate, least, times, right, size, bounded, product, finite, its, corresponding, denoting, cardinality, concerned, kinds, unlikely, events, move, precise, setup, simplest, coin, toss, step, you, either, win, loose, dollar, after, steps, having, than, dollars, where, fixed, course, goes, zero, playing, around, stirling, formula, reveals, decays, last, summer, attended, conference, numbers, max, planck, institute, bonn, vincent, delecroix, gave, talk, decided, learn, concept, time, spectral, series, lectures, due, faure, anantharaman, discussion, weyl, law, eigenvalues, rather, formalism, find, interesting, because, makes, assumption, metric, something, tool, connecting, statement, shnirelman, colin, verdière, zelditch, combines, way, several, compact, riemannian, geodesic, appropriately, normalized, measures, tend, weakly, usual, volume, home, skip, menu,

Text of the page (random words):
decus in labore decus in labore menu skip to content home about quantum ergodicity the quantum ergodicity theorem of shnirelman colin de verdière and zelditch is a result that combines in a nice way several different concepts namely suppose is a compact riemannian manifold with ergodic geodesic flow let be the appropriately normalized eigenfunctions of the laplacian then the measures with density tend weakly to the usual volume i find the result interesting because it makes a dynamical assumption on the metric and says something about the eigenfunctions of the laplacian the tool connecting these two aspects is microlocal analysis it appears in the proof but not in the statement of the result below the fold is a brief discussion of the main ideas that go into the proof weyl s law for the density of eigenvalues appears as a rather simple result of the general formalism of microlocal analysis i am following a series of lectures notes due to faure and anantharaman available here continue reading posted on february 28 2016 by simion tagged dynamical systems ergodic theory spectral theory leave a comment large deviations cramer s theorem last summer i attended a conference on dynamics and numbers at the max planck institute in bonn vincent delecroix gave a nice talk on large deviations for the teichmuller flow and i decided to learn a bit about this concept i wrote the notes below at that time in this post i will prove the simplest example of large deviations cramer s theorem here is a simple example consider a random coin toss and at each step you either win or loose dollar after steps consider the probability of having more than dollars where is fixed of course it goes to zero as but how fast playing around with stirling s formula reveals that the probability decays exponentially fast the theory of large deviations is concerned with these kinds of exponentially unlikely events we now move on to a more precise setup continue reading posted on october 24 2015 by simion tagged entropy probability leave a comment entropy and set projections let be a finite set and let be its projections to the corresponding two planes denoting by the cardinality of a set we have the following inequality this generalizes to sets in higher dimensions and projections to subspaces of possibly different dimensions as long as each coordinate appears at least times on the right the size of is bounded by the product of the projections one proof of the above inequality is via a mixed version of cauchy schwartz or holder type inequalities for functions of two variables we have taking to be indicators of projections of to the planes the bound follows however proving the inequality for requires some work there is a different inequality involving entropy of random variables whose proof and generalizations are much more conceptual namely if are random variables and denotes entropy we have below the fold are the definitions a proof and an application continue reading posted on september 11 2014 by simion tagged entropy leave a comment root systems in this post i will record some properties of reduced root systems following bourbaki the reference is their lie groups and algebras ch 4 6 there will be no proofs just a summary of the main properties the post consists mainly of definitions and lists their properties continue reading posted on september 10 2014 by simion tagged algebra bourbaki definitions leave a comment torsion on jacobians and teichmuller dynamics in this post i will describe a special case of a theorem about torsion points on jacobians and teichmuller dynamics which is proved in this paper namely i will describe a different proof of a theorem of moeller that for teichmuller curves zeroes of the holomorphic form must land in the torsion of a factor of the jacobian some familiarity with teichmuller dynamics will be assumed as in the survey of zorich continue reading posted on january 3 2014 by simion tagged algebraic geometry dynamical systems ergodic theory flat surfaces hodge theory rigidity leave a comment semisimplicity of the kontsevich zorich cocycle in this post i would like to discuss some of the ideas from my paper semisimplicity and rigidity of the kontsevich zorich cocycle it contains a number of somewhat disparate methods hodge theory random walks and a bit of homogeneous and smooth dynamics i will try to explain how these concepts interact and what the essential aspects are some familiarity with flat surfaces as explained for example in the survey by anton zorich will be assumed below the fold i will discuss some of the analytic ideas from variations of hodge structures then i ll try to connect these to teichmuller dynamics and explain how this leads to various semisimplicity results for applications i ll discuss how this implies that measurable invariant bundles have to be real analytic i ll also mention how real multiplication on factors of the jacobians arises continue reading posted on january 2 2014 by simion tagged dynamical systems ergodic theory flat surfaces hodge theory leave a comment grothendieck and the generalized hodge conjecture grothendieck famously wrote a paper called hodge s general conjecture is false for trivial reasons in this post i would like to record for my own benefit some of the observations made in it continue reading posted on july 13 2013 by simion tagged algebraic geometry grothendieck hodge conjecture 1 comment functions nice in each variable separately consider the following question if is continuous in each variable separately need it be continuous in both although cauchy incorrectly said it should note it is not even obvious that it should be measurable a classical example is defining this function is real analytic in each variable separately but it is not even continuous at the origin by contrast in the complex analytic situation we have the following result theorem 1 hartogs suppose is holomorphic in each variable separately then is holomorphic on below the fold i will state some more results of this type and prove some of them continue reading posted on july 8 2013 by simion tagged dynamics real analysis leave a comment descent for vector spaces in this note i would like to record mainly for my own benefit some basic things about how to descend algebraic data along galois extensions of fields i have benefited from some notes of k conrad available online the exposition below is a shorter version of those continue reading posted on april 30 2013 by simion tagged galois theory linear algebra leave a comment holomorphic bundles with hyperbolic fibers this brief note was inspired by this mathoverflow post a definition of a kobayashi hyperbolic manifold is available here informally it says that one can t holomorphically map arbitrarily large complex unit disks into the complex manifold in a certain sense most complex manifolds are kobayashi hyperbolic below is the proof of the following theorem of royden proved in this paper theorem 1 suppose is a holomorphic fibration with fiber a kobayashi hyperbolic manifold then the fibration is locally flat i e the gluing maps on overlapping local charts must be locally constant remark 1 the requirement that the fibration be holomorphic means that locally it is holomorphically isomorphic to for example if is the unit ball in the natural projection to the unit disk in is not a holomorphically trivial fibration one can see this using the maximum principle see the mo post for details continue reading posted on january 4 2013 by simion tagged complex manifolds flat bundles kobayashi hyperbolic rigidity leave a comment post navigation older posts search recent posts quantum ergodicity large deviations cramer s theorem entropy and set projections root systems torsion on jacobians and teichmuller dynamics archives february 2016 october 2015 september 2014 january 2014 july 2013 april 2013 january 2013 december 2012 november 2012 blogroll disquisitiones mathematicae geometry and the imagination what s new terry tao follow blog via email enter your email address to follow this blog and receive notifications of new posts by email email address follow follow decus in labore on wordpress com blog at wordpress com decus in labore proudly powered by wordpress theme publish by konstantin kovshenin subscribe subscribed decus in labore sign me up already have a wordpress com account log in now privacy decus in labore subscribe subscribed sign up log in report this content view site in reader manage subscriptions collapse this bar loading comments write a comment email required name required website design a site like this with wordpress com get started

Thumbnail images (randomly selected): * Images may be subject to copyright.

Decus in Labore
(M,g)
$Images may be subject to copyright. Alt Attribute (original): \ \phi_k\$
\ \phi_k\
$Images may be subject to copyright. Alt Attribute (original): \Delta$
\Delta
$Images may be subject to copyright. Alt Attribute (original): \frac 1 N\sum_ k=1 ^N \phi_k ^2 \cdot d \mathrm Vol$
\frac 1 N\sum_ k=1 ^N \...
$Images may be subject to copyright. Alt Attribute (original): d \mathrm Vol$
d \mathrm Vol
1
N
aN
a 0
$Images may be subject to copyright. Alt Attribute (original): N \rightarrow \infty$
N \rightarrow \infty
$Images may be subject to copyright. Alt Attribute (original): A\subset \mathbb Z ^3$
A\subset \mathbb Z ^3
A_ xy , A_ yz , A_ xz
$Images may be subject to copyright. Alt Attribute (original): \# S$
\# S
S
$Images may be subject to copyright. Alt Attribute (original): \displaystyle \left(\# A\right)^2 \leq \left(\# A_ xy \right)\left(\# A_ yz \right) \left(\# A_ xy \right)$
\displaystyle \left(\# A...
n
$Images may be subject to copyright. Alt Attribute (original): \left(\# A\right)^n$
\left(\# A\right)^n
f,g,h
$Images may be subject to copyright. Alt Attribute (original): \displaystyle \begin array rcl \left(\int \int \int f\left(x,y\right) g\left(y,z\right) h\left(x,z\right) dx\, dy\, dz\right)^2 \leq\\ \leq\left(\int \int f\left(x,y\right)dx\, dy\right) \cdot \le...$
\displaystyle \begin arr...
A
2
X,Y,Z
$Images may be subject to copyright. Alt Attribute (original): H\left(-\right)$
H\left(-\right)
$Images may be subject to copyright. Alt Attribute (original): \displaystyle 2H\left(X,Y,Z\right) \leq H\left(X,Y\right) + H\left(Y,Z\right) + H\left(X,Z\right)$
\displaystyle 2H\left(X,...
$Images may be subject to copyright. Alt Attribute (original): \mathrm SL _2 \mathbb R$
\mathrm SL _2 \mathbb ...
$Images may be subject to copyright. Alt Attribute (original): f: \mathbb R ^2\rightarrow \mathbb R$
f: \mathbb R ^2\rightarr...
$Images may be subject to copyright. Alt Attribute (original): \displaystyle f(x,y):= \frac xy x^2+y^2$
\displaystyle f(x,y):= \...
f(0,0)=0
$Images may be subject to copyright. Alt Attribute (original): f: \mathbb C ^ n_1 \times \mathbb C ^ n_2 \rightarrow \mathbb C$
f: \mathbb C ^ n_1 \time...
f
$Images may be subject to copyright. Alt Attribute (original): \mathbb C ^ n_1+n_2$
\mathbb C ^ n_1+n_2
$Images may be subject to copyright. Alt Attribute (original): E\rightarrow B$
E\rightarrow B
F
$Images may be subject to copyright. Alt Attribute (original): U\times F$
U\times F
$Images may be subject to copyright. Alt Attribute (original): \mathbb B =\ (z,w)\in \mathbb C ^2 \rvert z ^2+ w ^2$
\mathbb B =\ (z,w)\in ...
$Images may be subject to copyright. Alt Attribute (original): \mathbb C ^2$
\mathbb C ^2
$Images may be subject to copyright. Alt Attribute (original): \mathbb B \rightarrow \mathbb D$
\mathbb B \rightarrow ...
$Images may be subject to copyright. Alt Attribute (original): \mathbb C$
\mathbb C

Verified site has: 44 subpage(s). Do you want to verify them? Verify pages:

1-5

6-10

11-15

16-20

21-25

26-30

31-35

36-40

41-44

The site also has references to the 5 subdomain(s)

matheuscmss.wordpress.com	Verify	lamington.wordpress.com	Verify	terrytao.wordpress.com	Verify
wordpress.com	Verify	subscribe.wordpress.com	Verify

The site also has 8 references to external domain(s).

en.wikipedia.org	Verify	math.polytechnique.fr	Verify	arxiv.org	Verify
ams.org	Verify	mathoverflow.net	Verify	encyclopediaofmath.org	Verify
wordpress.org	Verify	kovshenin.com	Verify

site address: decusinlabore.wordpress.com redirected to: decusinlabore.wordpress.com

site title: Decus in Labore

Header

Meta Tags

Load Info