Peter scholze blog

Peter scholze blog. It takes values in a mixed-characteristic analogue of Dieudonné modules, which was previously defined by Fargues as a version of Breuil–Kisin modules. Continue reading →. First Lecture: October 18, 2023. We deduce the weight-monodromy conjecture in certain cases by reduction to Jun 7, 2013. Posted on July 7, 2023 by woit. Jul 28, 2023 · In 2018 things finally came to a head when mathematician Peter Scholze and his colleague Jakob Stix published the paper “Why ABC Is Still a Conjecture. Papers/Preprints. 7. ) - 12 Uhr, und Fr, 10 (c. Prismatic F-crystals and crystalline Galois representations (with Bhargav Bhatt), Preprint, 2021. Emmy Noether LecturesTopic: Real local Langlands as geometric Langlands on the twistor-P^1Speaker: Peter ScholzeAffiliation: Max-Planck-Institut für Mathemat Aug 1, 2018 · The Fields Medal is considered the Nobel Prize of mathematics, and this year the International Mathematical Union chose to award it to Peter Scholze. Similarly, a condensed group, condensed ring, etc. Motivated by problems on the étale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the étale cohomology of diamonds, and more generally small v-stacks on the Mar 31, 2024 · In Global character of ABC/Szpiro inequalities, Peter Scholze says that he thinks Joshi's proof of the abc conjecture in his paper has a mistake in Proposition 6. He has been called one of the leading mathematicians Jan 20, 2024 · [This is a guest post by Peter Scholze. Email: scholze@mpim-bonn. That means Dr. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings’ almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and characteristic p. NT) [24] arXiv:1205. Relative Perversity (with David Hansen), Preprint, 2021. We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. Oct 18, 2023 · Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location. 2020. Mi, 10 (c. Facebook gives people the power to Jul 3, 2016 · The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry. Feb 9, 2018 · Inspired by a theorem of Bhatt-Morrow-Scholze, we develop a stacky approach to crystals and isocrystals on "Frobenius-smooth" schemes over F_p . For extensive background on this, you could start at this blog posting and work backwards, to Prof. com Peter Scholze (German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ⓘ; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. To submit Peter Scholze is recognised as the leading mathematician of his generation in the field of arithmetic geometry. Aug 10, 2012 · Abstract. Mark Kisin gave a talk at the number theory seminar last week where the following problem arose: Let W be the Galois representation associated to the Tate module of an abelian variety A over a number field, and suppose that W = U ⊗ V. t. Another new ingredient is the pro-etale site, which makes all constructions completely functorial. Jun 19, 2017 · A double honor for an exceptional mathematical talent: The renowned German National Academy of Sciences Leopoldina has elected Peter Scholze, professor at the Cluster of Excellence Hausdorff Center for Mathematics at the University of Bonn, to become a member. 2016. The idea is to develop the geometric Langlands program on the Fargues-Fontaine curve, using the Feb 22, 2021 · Some months ago, Peter Scholze wrote a guest post on the Xena-blog: Liquid tensor experiment, proposing a challenge to formalise the proof of one of his results with Dustin Clausen on condensed mathematics. : 0228-73-62216 E-mail: ja (ergänze @math. After working about the cohomology of Shimura varieties and the Langlands program, his PhD thesis was about a theory of perfectoid spaces, which gives a method to compare objects in mixed characteristic with objects in equal Jul 21, 2022 · I will speak about my joint work about the geometrization of the local Langlands correspondence. In fact, starting with a \ (p\) -adic variety, localizing to make it perfectoid, passing to its tilt, and then “delocalizing” this tilt can be made canonical. We show that there exist functors from the category of condensed sets to Diamonds are a beautiful class of geometric objects introduced by Peter Scholze in his course at Berkeley in the Fall of 2014. Thus, in this case the assertion is only true up to sign, but for example if k v is a nonarchimedean localization, it becomestrueifonereplacesk by o k v Oct 7, 2010 · Peter Scholze. Oct 2, 2023 · Prismatic cohomology is a cohomology theory for p-adic formal schemes which can specialize into various p -adic cohomology theories, including étale cohomology, de Rham cohomology and crystalline cohomology, as well as the so far conjectural q -de Rham cohomology of Peter Scholze. At a few points, we have expanded slightly on the material, in particular so as to provide a full construction of local Shimura varieties and general moduli spaces of shtukas, Semantic Scholar profile for P. The resulting cohomology theory specializes to (and often refines) most known Mar 21, 2024 · In the recent lecture series run jointly from IHÉS and Bonn, Clausen and Scholze have reworked—again—their foundations of geometry to focus attention on not arbitrary condensed sets and solid modules and so on, but the much smaller class of light condensed sets and so on. Peter Scholze, Jared Weinstein. This class of schemes goes back to Berthelot-Messing … Expand Tuesdays, 10:15 -- 12:00, Kleiner Hörsaal. Let me end by saying that I wished that Mochizuki had focused his manuscript only on this mathematical point, and that I feel deeply sorry for Joshi for the rest of the manuscript (and more generally, I feel deep embarassment as a member of the mathematical community). I've just come across a Twitter thread by Laurent Fargues explaining a work by Dustin Clausen & Peter Scholze under the name Condensed Mathematics and how Condensed Mathematics can algebraize topology and analysis. Posted on October 19, 2023 by woit. We deduce the weight-monodromy conjecture in certain cases by reduction to equal Feb 26, 2021 · We study the étale cohomology of Hilbert modular varieties, building on the methods introduced by Caraiani and Scholze for unitary Shimura varieties. This evening on the arXiv James Arthur has posted a wonderful 204 page document explaining the work of Robert Langlands, written in conjunction with the award of the Abel Prize …. This raises the question of a similar realization of the local Langlands correspondence over the real numbers. 3463 [ pdf, ps, other] May 20, 2019 · Prisms and Prismatic Cohomology. In July 2019 he established that the field of functional analysis still works if one replaces conventional topological spaces with condensed sets. Peter Scholze. After working about the cohomology of Shimura varieties and the Langlands program, his PhD thesis was about a theory of perfectoid spaces, which gives a method to compare objects in mixed characteristic with objects in equal Perfectoid Spaces: A survey. ] Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin Clausen. Peter Scholze obtained his PhD in 2012 under the supervision of Michael Rapoport at the Universität Bonn. Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years. 027 Tel. 皮特·舒尔策（德語： Peter Scholze ，德语发音： [ˈpʰeːtʰɐ ʃɔlʦə] ，1987年12月11日 — ），德国算术代数几何学家，数学领军人之一 。 他提出了 状似完备空间 （ 英语 ： perfectoid space ） 理论，并在 动机 （ 英语 ： Motive (algebraic geometry) ） 理论和 朗兰兹纲领 这 Sep 20, 2018 · September 20, 2018. For more about why one attempted proof doesn’t work, see here and here. Proof. The main purpose of this paper is to investigate in which way the theory of homotopy groups on topological spaces can be extended to the theory of condensed sets. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Moreover, we define a refined fundamental group of schemes, which is large enough to see all lisse ℓ -adic sheaves, even May 15, 2012 · p-adic Hodge theory for rigid-analytic varieties. de) Time and Place . This course will cover basic scheme theory. is defined as a sheaf of groups, rings etc. The Fields Medal is awarded to recognize outstanding mathematical achievement for existing work and for the promise of future achievement. As usual at an Arbeitstagung, part of the program will only be decided during the event depending on the interests of the audience. Edit: Forgot to say, Bonn also has a fast-tracked graduate school for gifted students. Fields Medals 2018. The goal of these lectures is to explain a possible formulation Jun 5, 2021 · We would like to show you a description here but the site won’t allow us. There is a fantastic set of notes available from this course (“the Berkeley notes”). The medal, first awarded in Nov 4, 2023 · Peter Scholze, Liquid tensor experiment, December 2020. The present document grew out of my attempts to understand various particular claims in the Berkeley notes, and various other questions about diamonds. Nov 21, 2011 · Perfectoid Spaces. Peter Scholze (Univ. the category ProFin ˘= Pro(Fin) of pro nite sets S with covers given by nite families of jointly surjective maps. These are enough to faithfully capture all sequential spaces, for Apr 3, 2020 · Two German mathematicians — Peter Scholze at the University of Bonn and Jakob Stix at Goethe University, Frankfurt — privately circulated a rebuttal of his abc proof, zeroing in on one crucial Fax: +49 (0)228 402-277. Lecture II: Liquid vector spaces 11 . To any topological space one can associate a condensed set, customarily denoted Akhil Mathew. Nov 8, 2015 · Ana Caraiani, Peter Scholze. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of p-adic Hodge theory. The goal of this course is to give an overview of the approach of Laurent Fargues and myself on the local Langlands correspondence. This relies on the theory of perfectoid spaces. p p -adic Hodge Theory for rigid spaces, after P. AG); Number Theory (math. Scholze and Clausen ran a masterclass in Copenhagen on condensed mathematics, which you can binge watch on YouTube starting here Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germanyscholze@math. While this challenge has not been completed yet, I am excited to announce that the 1. PETER SCHOLZE Abstract. To any scheme, one can associate its derived category of l-adic sheaves, and this comes equipped with six operations: Tensor product and internal Hom; pullback and pushforward; proper pushforward and exceptional inverse image. Sep 14, 2023 · Peter wrote: “Scholze’s talk gave a speculative picture of how to think about the global arithmetic story, with Spec(ℤ) as a sort of three-dimensional space. Tomorrow Andrew Wiles will be giving a talk in Oxford on “A New Approach to Modularity”, with abstract: Peter Scholze response to Joshi's manuscripts. His contributions include descent and Jun 19, 2023 · The Arbeitstagung 2023 will focus on Condensed Mathematics, a new approach to topology, and its applications throughout mathematics, from logic over algebra, analysis and K-theory to group theory and dynamical systems. To submit Aug 24, 2023 · Million Dollar Prize for Scholze and Stix Posted on July 7, 2023 by woit At a news conference in Tokyo today there evidently were various announcements made about IUT, the most dramatic of which was a 140 million yen (roughly one million dollar) prize for a paper showing a flaw in the claimed proof … Jul 7, 2023 · Million Dollar Prize for Scholze and Stix. We obtain the analogous vanishing theorem: in the … Expand Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. Dr. 3 days ago · In Bonn, Peter Scholze is running a seminar on Real local Langlands as geometric Langlands on the twistor-P1. Consider the pro- etale site pro et of the point , i. Johannes Anschütz Endenicher Allee 60 · Zimmer 4. Tuesday, 10-12h, Großer Hörsaal Thursday, 10-12h, Kleiner Hörsaal First Lecture: Tuesday 18. LECTURE I: INTRODUCTION 7 Definition 1. Posted on March 18, 2024 by woit. Mar 4, 2021 · ABC is Still a Conjecture. Now suppose that the Galois action on U is unramified at all primes above p. (2018年3月20日) 事实速览 皮特·舒爾策Peter Scholze, 出生 皮特·舒尔策，德国算术代数几何学家，数学领军人之一。. Subjects: Algebraic Geometry (math. Scholze in Fall 2014 at UC Berkeley. C. V5A5: Geometrization of the local Langlands correspondence. 1. Mar 6, 2024 · Sponsored by the Minerva Research Foundation. Pereira Lourenço, João Nuno. de Dustin Clausen, Peter Scholze. ” In it, they claimed to have found a Aug 1, 2018 · Number theorist Peter Scholze, who became Germany’s youngest ever full professor aged 24, and geometrician Caucher Birkar—a Kurdish refugee—are among the winners of this year’s Fields 6 PETER SCHOLZE AND JAKOB STIX that commute with this injection: The automorphisms of the latter are just Zb , and except for 1, these do not respect the subset k along the above inclusion6. [3] [4] He won the Fields Medal in 2018. If you have additional information or corrections regarding this mathematician, please use the update form. E-Mail: scholze@mpim-bonn. We deduce the weight-monodromy conjecture in certain cases by reduction to equal May 26, 2020 · In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p -adic geometry. Geometrization of the local Langlands correspondence (with Laurent Fargues), Preprint, 2021. Born 1987. 3463 [ pdf, ps, other] Sep 21, 2017 · Etale cohomology of diamonds. 10. I find it somewhat surprising (or hard to believe) that you can do such a thing. Just a reminder that the abc conjecture is still a conjecture, there is no known valid proof (don’t believe what you might read in an EMS journal ). His achievements have already been recognized by a number of prizes and honors. Lecture I: Introduction 6 2. Scholze, with 474 highly influential citations and 99 scientific research papers. The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Rheinische Friedrich-Wilhelms-Universität Bonn. Homology of PGL2(F) P G L 2 ( F) Apr 20, 2018. 2022. Videos of talks from a conference on arithmetic geometry in honor of Helene Esnault at the IHES last week are now available. Here’s the syllabus: The purpose of this course is to propose new foundations for analytic geometry. The 30-year Peter Scholze is a new director at the Max Planck Institute for Mathematics. Aug 1, 2018 · By custom, Fields medals are bestowed to mathematicians 40 years old or younger. ” While there’s speculation in Scholze’s talk, I want to let beginners know that the 3-dimensional nature of Spec(ℤ) is not a speculative thing. Contents Condensed Mathematics and Complex Geometry 5 Preface 5 1. uni-bonn. Not sure if they have the same for undergrad. on this site. It is a geometric approach to integral p-adic Hodge theory. He has been called one of the leading mathematicians in the world. In 2014, Fargues realized that one can formulate the local Langlands correspondence over p-adic fields as a geometric Langlands correspondence on the Fargues-Fontaine curve. 44. At a news conference in Tokyo today there evidently were various announcements made about IUT, the most dramatic of which was a 140 million yen (roughly one million dollar) prize for a paper showing a flaw in the claimed proof of the abc conjecture. According to our current on-line database, Peter Scholze has 3 students and 3 descendants. 他提出了状似完备空间理论，并在动机理论和朗兰兹纲领这两个代数几何学的大方向上有杰出贡献。. We welcome any additional information. Oct 30, 2019 · Scholze showed that locally for a suitable topology (the pro-étale topology, see 5 below) every classical \ (p\) -adic variety is indeed perfectoid. View the profiles of people named Peter Scholze. Akhil Mathew received his PhD from Harvard in 2017 and was a Clay Research Fellow from 2017 to 2022. The professor at the University of Bonn’s Hausdorff Center for Mathematics and Director at the Max Planck Institute for Mathematics was presented with the award during the International Congress of Mathematicians in Rio de Janeiro. His point of view has enabled him to make progress on some of the best known problems in this and neighbouring fields. ) - 12 Uhr, MPI-Hörsaal. May 17, 2021 · The theory of condensed mathematics by Dustin Clausen and Peter Scholze claims that topological spaces should be replaced by the definition of condensed sets. mpg. Fields at the University of Toronto, which has been supplemented periodically, but is still significantly underfunded. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what 3 days ago · 20 Years of Not Even Wrong. Moreover, the Bonn-based exceptional mathematician also became a member of the Berlin Sep 4, 2019 · View a PDF of the paper titled On the generic part of the cohomology of non-compact unitary Shimura varieties, by Ana Caraiani and Peter Scholze View PDF Abstract: We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree Apr 14, 2022 · 7. Feb 28, 2024 · A New Approach to Modularity. It then consists of many coherences - these are isomorphisms between certain compositions of these functors You only need 180ECTS to get a bachelor degree, and considering his background, his parents and his intellect, I would assume that he was taking university level classes way before he officially enrolled. The text below is a slightly edited version of the blog post Xena Project – Liquid Tensor Experiment, and I have kept its informal style. Perfectoid Spaces: A survey. Back when I started this up, blogging …. In May 9, 2024 · Posted on May 9, 2024 by Persiflage. Feb 9, 2016 · We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of Cp$\mathbf {C}_{p}$. Studies of Mathematics at the University of Bonn, Master 2010, PhD 2012. Peter Scholze is recognised as the leading mathematician of his generation in the field of arithmetic geometry. Sep 4, 2013 · The pro-étale topology for schemes. ”. Jun 20, 2021 · The text below is a slightly edited version of the blog post Xena Project – Liquid Tensor Experiment, and the informal style has kept its informal style. The 30-year old is one of the leading researchers in the field of Arithmetic Geometry. de. This is more of an advertisement than a blog post. Peter Scholze - Mathematisches Institut der Universität Bonn. Bonn and Max Planck Institute Research Area Algebraic geometry Visit Tuesday, March 12, 2019 to Thursday, March 14, 2019 Location MS 5200 Jul 30, 2021 · The specific result was by Peter Scholze of the University of Bonn, a mathematician with very impressive credentials, including the 2018 Fields Medal, arguably the highest honor in mathematics. 他于2018年获得菲尔兹奖 Apr 2, 2014 · Lecture: Locally symmetric spaces, and Galois representationsSpeaker: Peter Scholze (The University of Bonn, Germany)Date: 25 Mar 2014, 11:30 AMVenue: AG 66 Peter Scholze - Mathematisches Institut der Universität Bonn. The medals and cash prizes are funded by a trust established by J. Applications of condensed mathematics include the following: Laurent Fargues, Peter Scholze, Geometrization of the local Langlands correspondence (arXiv:2102. Jul 19, 2021 · Peter Scholze, a mathematician at the University of Bonn, has co-authored a paper that introduces a new geometric object called the Fargues-Fontaine curve. He has introduced new ideas to this field, most notably the theory of perfectoid spaces. We reprove the Local Langlands Correspondence for $\GL_n$ over p -adic fields as well as the existence of ℓ -adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book of Harris-Taylor. Peter Scholze's 66 research works with 2,817 citations and 6,203 reads, including: Purity for flat cohomology The text below is a slightly edited version of the blog post Xena Project Mar 25, 2024 · Million Dollar Prize for Scholze and Stix Posted on July 7, 2023 by woit At a news conference in Tokyo today there evidently were various announcements made about IUT, the most dramatic of which was a 140 million yen (roughly one million dollar) prize for a paper showing a flaw in the claimed proof … Peter Scholze (born 11 December 1987 [2]) is a German mathematician known for his work in arithmetic geometry. Zoom Link (Password: 069444) Zuletzt geändert: October 2023, Peter Scholze. Jan 13, 2018. Fax: +49 (0)228 402-277. The topics covered are as follows: Peter Scholze. The first entry on this blog was 20 years ago yesterday, first substantive one was 20 years ago tomorrow (first one that drew attacks on me as an incompetent was two days later). We introduce the notion of a prism, which may be regarded as a "deperfection" of the notion of a perfectoid ring. Peter Scholze Contact: Dr. Aug 1, 2018 · Number theorist Peter Scholze, who became Germany’s youngest ever full professor at the age of 24, and geometrician Caucher Birkar — a Kurdish refugee — are among the winners of this year Mar 11, 2023 · The six functor formalism in a given cohomology theory consists of for each space a derived category of sheaves and six different ways to construct functors between those categories (four involving a morphism and two only a single space). Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. Bhargav Bhatt, Peter Scholze. Update: One more item. We prove several results about p-divisible groups and Rapoport-Zink spaces. Comments: 38 pages, survey for the Proceedings of the 2012 conference on Current Developments in Mathematics. We give a new definition of the derived category of constructible ℓ -adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Along the way, we establish various foundational results on the Peter Scholze. Join Facebook to connect with Peter Scholze and others you may know. 37. In particular his ideas Fax: +49 (0)228 402-277. I was assuming that Peter Scholze’s Emmy Noether lectures at the IAS would be the big news about advances in the Langlands program this coming week, but an anonymous correspondent just sent me this link. Apr 3, 2020 · @Peter Scholze, April 14, 2020 at 5:17 pm >The remarks from IUT that you cite make heavy reference to his paper on etale theta-functions, which seems to play a key role in the IUT papers. Hausdorff Chair, University of Bonn, since October 2012. Using prisms, we attach a ringed site -- the prismatic site -- to a p -adic formal scheme. Peter Scholze, Half a year of Liquid Tensor Experiment: Amazing developments, June 2021. Abstract I propose a formalization challenge. Purity for flat Apr 28, 2024 · The Work of Robert Langlands. my blog Rampage seminar (2020-2022) p-adic geometry, d'apres Peter Scholze Notes from an informal lecture series I gave at Columbia in Spring 2015, on Scholze's Dec 21, 2019 · How did Peter Scholze learn math? Scholze started teaching himself college-level mathematics at the age of 14, while attending Heinrich Hertz Gymnasium, a Berlin high school specializing in mathematics and science. Content of the course . Scholze. Purity for flat Peter Scholze ( German pronunciation: [ˈpeːtɐ ˈʃɔltsə] ⓘ; born 11 December 1987 [2]) is a German mathematician known for his work in arithmetic geometry. U. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. The idea of a six-functor formalism emerged in the study of etale cohomology. Mathew's research interests are in algebraic K-theory, topological cyclic homology, and p -adic geometry. 7, Kirti Joshi merely says that. Shinichi Mochizuki maintains that his proof is not flawed despite the assertions of Jakob Stix and Peter Scholze that they’ve discovered a “serious, unfixable gap. This paper gives some neat algorithm to start from the fundamental group of a once-punctured elliptic curve with bad semistable reduction, and recover its See full list on nature. Nov 27, 2012 · Moduli of p-divisible groups. 13459) 此條目需要擴充。. A condensed set is a sheaf of sets on the site of profinite sets, with the Grothendieck topology given by finite, jointly surjective collections of maps. e. Scholze would have still been eligible for another two rounds of medals. At Heinrich Hertz, Scholze said, “you were not being an outsider if you were interested in mathematics. Dustin Clausen and Peter Scholze are giving a course together this fall on Analytic Stacks, with Clausen lecturing at the IHES, Scholze from Bonn. He was appointed as an Associate Professor at the University of Chicago in 2022. This curve connects number theory and geometry as part of the Langlands program, a sweeping project that seeks to link different branches of mathematics. In particular his ideas Oct 19, 2023 · Analytic Stacks. This is a revised version of the lecture notes for the course on p-adic geometry given by P. These notes undoubtedly Peter Scholze - Max Planck Insitute for Mathematics. Clay Research Fellow 2011-2016. Jul 3, 2016 · The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry. However, for the proof of Proposition 6. Posted on July 6, 2023 by woit. Bonn)Laurent Fargues (IMJ-PRG) 2022. Chancellor's Professor, UC Berkeley, Fall 2014. li gp cf bu dt sz nl ij uu yp