Related papers: IMPANGA lecture notes on log canonical thresholds
Building on results of Koll\'ar, we prove Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties, and more generally, on varieties with quotient singularities.
We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.
We give a method to investigate isolated log canonical singularities with index one which are not log terminal. Our method depends on the minimal model program. One of the main purposes is to prove that our invariant coincides with Ishii's…
These lectures provide an introduction to effective theories concentrating on the basic ideas and providing some simple applications
This is a short note on the log canonical inversion of adjunction.
This short note is the extended abstract of a seminar I have delivered on several occasions over the past few months on canonical threefolds whose canonical volume is "close" to the lower bound 4/3p_g - 10/3. This is a project in…
We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
It is proved that the global log canonical threshold of a Zariski general Fano complete intersection of index 1 and codimension $k$ in ${\mathbb P}^{M+k}$ is equal to one, if $M\geqslant 2k+3$ and the maximum of the degrees of defining…
Lectures on Quantum Coulomb gases delivered at the CIME summer school on Quantum Many Body Systems 2010
We study the \L ojasiewicz exponent and the log canonical threshold of ideals of $\mathcal O_n$ when restricted to generic subspaces of $\mathbb C^n$ of different dimensions. We obtain effective formulas of the resulting numbers for ideals…
These are the notes of a course on Shimura varieties that I gave at the 2022 IHES summer school on the Langlands program. Lecture 1 gives an introduction to Shimura varieties over the complex numbers (defined here as a special type of…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
These notes provide an overview of various notions of hyperbolicity for varieties of log general type from the viewpoint of both arithmetic and birational geometry. The main results are based on our paper entitled "Hyperbolicity and…
We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…
In this paper we show that the global (log) canonical threshold of $d$-sheeted covers of the $M$-dimensional projective space of index 1, where $d\geqslant 4$, is equal to one for almost all families (except for a finite set). The varieties…
These are the lecture notes of a course taught at the Park City Mathematics Institute in June 2017. They are intended to review some recent results, obtained in large part with Thomas Lebl\'e, on the statistical mechanics of systems of…
We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We…
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.