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Nature Computational Science 1 (6), 403-409, 2021. After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water. You can decide this piece goes here, that piece goes there. So, in this article, we discussed all information about Alessio Figalli's net worth, wiki, bio, career, height, weight, family, pics, affairs, car, salary, age, and other details in 2023.
Workshop in honor of Alessio Figalli's Doctor Honoris Causa at UPC Articles Cited by Public access Co-authors.
48 Alessio Figalli Premium High Res Photos - Getty Images Alessio Figalli - Viquipdia, l'enciclopdia lliure He was born on 2 April 1984, in Rome, Italy, .Rome is a beautiful and populous city located in Rome, Italy. Title. You might be interested to know more about Alessio Figalli. But when Caffarelli zoomed in on the frozen boundary between ice and water, he sometimes saw something totally different: frozen spots surrounded almost entirely by warmer water. Woods Memorial Prize for being the leading graduating student of the year. You can make your unit of transport infinitely small in your quest to find the optimal way to move material around and this is where analysis comes in, as an extended form of calculus, the study of change on infinitely small or large scales. This is one of those problems that naturally exhibits singularities, said Giuseppe Mingione of the University of Parma. The book is suitable for a . At Akshays request I explained what the problem was. Yet Figalli, Ros-Oton and Serra realized that very similar singularities form along the melting boundary between ice and water. It takes a lot of different traits to be a successful mathematician technical skill, ingenuity, an ability to persevere under great uncertainty. They go beyond the parabolic scaling, said Sandro Salsa of the Polytechnic University of Milan. Personal touch and engage with his followers. Alessio Figalli has a net worth of $5.00 million (Estimated) which he earned from his occupation as Mathematician. In 1998, under Peter Sarnak, he commenced his PhDat the age of 17 at Princeton University, which he completed in 2002 at the age of 21. The equations work well, but its taken 130 years to prove that they conform to obvious facts about reality. The birthday of Alessio Figalli is on 2-Apr-1984. Please agree and read more about our, A Traveler Who Finds Stability in the Natural World. Caffarelli had made progress on understanding how singularities develop as ice melts, but there was a feature of the process he didnt know how to address. Mathematicians regularly come to ETH in Zurich to share new ideas situated at the boundaries of mathematical knowledge. Va ser un dels conferenciants convidats al Congrs Internacional de Matemtiques (ICM), el 2014. Alessio Figalli's income source is mostly from being a successful .
Alessio Figalli2018fields__bilibili In addition, he has given several contributions to the Di PernaLions theory, applying it both to the understanding of semiclassical limits of the Schrdinger equation with very rough potentials, and to study the Lagrangian structure of weak solutions to the VlasovPoisson equation. He is from Italian. But remarkably, Caffarelli found that as you move away from the singularity, the temperature increases in a clear pattern: If you move one unit in distance away from a singularity and into the water, the temperature rises by approximately one unit of temperature. Mathematicians model this melting process with equations. Alessio Figalli (born 2 April 1984) is an Italian mathematician working primarily on calculus of variations and partial differential equations. The Stefan problem is a foundational example for an entire subfield of math where boundaries move. With his large number of social media fans, he often posts many personal photos and videos to interact with his huge fan base on social media platforms. Focus in on an arbitrary point on the films surface. Figalli was fascinated to discover that there were math problems whose solutions were not straightforward you had to invent them yourself. The circle is a simple example of a minimal surface in that its the shape that minimizes the perimeter required to enclose some amount of area. Mathematicians devised a method for zooming in on the point, as though they had a microscope with infinite power. Which is why
ERC grantee Alessio Figalli receives a 2018 Fields Medal for Email us at [emailprotected], Some Lesser Known Facts About Akshay Venkatesh, Priyanka Paul Height, Age, Boyfriend, Family, Biography & More, Melinda Gates Age, Boyfriend, Husband, Family, Biography & More, Sweety Walia (Actress) Age, Husband, Family, Biography & More, Mahira Sharma Age, Boyfriend, Family, Biography & More, Lee Min-ho Height, Age, Girlfriend, Wife, Family, Biography & More, Daman Singh (Manmohan Singhs Daughter) Wiki, Age, Family, Biography & More, Shubhi Sharma (Actress) Height, Weight, Age, Boyfriend, Biography & More, Karishma Modi Height, Weight, Age, Husband, Children, Biography & More, Winning Mathematics prestigious Fields Medal, known as the Nobel prize for math, Perth, Australia (lives in the United States), First Class Honours in Pure mathematics from the University of Western Australia in 1997, Does Akshay Venkatesh drink alcohol? Figallis quickness is something many of his colleagues remark on both the quickness with which he works through technical details and the speed with which he understands the crux of a new problem. Workshop in honor of Alessio Figalli's Doctor Honoris Causa at UPC Five talks and a Round Table with Prof. Alessio Figalli. The idea originated in the 18th century, when a mathematician working for Napoleon Bonaparte tried to find the most efficient way to build a network of earthen fortifications. Alessio FigalliDurham University Mikaela IacobelliETH | Tom Parker /QuantaMagazine Figalli Figalli () Suppose you have a solution to the soap film equations that describes the shape of the film between two boundary surfaces, like the set of two rings. Figallis second major result had a similar flavor. This is called a parabolic relationship, because if you graph temperature as a function of distance, you get approximately the shape of a parabola. The Stefan problem became a problem of showing that the singularities in these situations are actually well controlled. Save my name, email, and website in this browser for the next time I comment. In this section, we will talk about Alessio Figalli's personal life, life story. I came from classics, my high school was not a scientific one, I was studying Latin, Greek, Philosophy, everything but Maths. These results open a new perspective on the field, said Maria Colombo of the Swiss Federal Institute of Technology Lausanne. My career just came naturally from that. In 2009 he moved to the University of Texas at Austin as associate professor. To solve the Stefan problem, Figalli, Ros-Oton and Serra needed to prove that singularities that crop up in the equations are controlled: There arent a lot of them and they dont last long. But with a little imagination, it is easy to conceive of scenarios where sharp spots emerge. In 1994, after being at second place in the Australian Mathematical Olympiad, Venkateshwon a silver medal in the 6th Asian Pacific Mathematics Olympiad. Monge made some headway on the problem, but then it languished for more than a century. They are a way of validating the mathematical representations of physical phenomena. When physicists say a soap bubble is stable, they mean that if you nudge it slightly, it only wavers slightly the nudge doesnt induce a dramatic change in shape. Alessio Figalli in 1989 at age 5, as a kindergartener at the Padre Lais school in Rome. The mathematicians say that the technical details of the work will take time to digest. Lecture Notes in Mathematics 2171 Steve Wright Quadratic Residues and Non-Residues Selected Topics Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Michel Brion, Grenoble Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark . At certain points, the researchers managed to zoom in to find an analogous scenario: two fronts of ice collapsing toward the point as if it were situated inside a thin sheet of ice. Famously known by the Family name Alessio Figalli, is a great Mathematician.
Alessio Figalli - Wikipedia Optimal transport is so intuitive that its easy to overlook the mathematical complexity it contains. Figalli and De Philippis thought about the optimal transport map that converts the initial shape and position of a front into its subsequent shape and position. Abstract. Find Alessio Figalli stock photos and editorial news pictures from Getty Images. Amongst these is European Research Council grantee Prof. Alessio Figalli working at ETH Zrich (Switzerland), who received an ERC Consolidator Grant in 2016. He is rarely there for more than two weeks at a time. Mathematicians wanted to use the same methods to deal with the Stefan problem, but they soon realized that with ice, things were not as simple. The young Italian mathematician is tall, fit and stylish, his Rs rolling off the tongue with an intoxicating Roman richness. He was awarded the Prix and Cours Peccot[fr] in 2012, the EMS Prize in 2012,[1] the Stampacchia Medal in 2015,[2] the Feltrinelli Prize in 2017, and the Fields Medal in 2018. Courtesy of Alessio Figalli "For me it was always a balance between how good a grade I could get and how much time I had to spend to get such a grade," he said. Figalli, Ros-Oton and Serra shifted the microscope onto this deviation from the paraboloid pattern. 2007-yil Luigi Ambrosio rahbarligida Pisadagi Oliy normal maktabdan hamda Cdric Villani rahbarligida .
Alessio Figalli Biography, Age, Height, Wife, Net Worth, Family Alessio Figalli198442- 2012Prix and Cours Peccot[1]2015Stampacchia[2]2017Feltrinelli2018 2014[3] 2016(ERC)2018 [] Having shown that the exotic branching and sheetlike singularities were both rare, the researchers could make the general statement that all singularities for the Stefan problem are rare. Mathematical knowledge plays a key role in this transition. Personal Homepage of Prof. Dr. Alessio Figalli Curriculum vitae Personal information Born: April 1984, Rome (Italy) Languages: Italian (native), English and French (fluent), Spanish (intermediate), German (basic) Citizenship: Italian citizen, Swiss permanent resident Civil status: married Download full CV as PDF Download short CV as PDF More recently, in collaboration with Alice Guionnet, he introduced and developed new transportation techniques in the topic of random matrices to prove universality results in several-matrix models. Anthony Ledford. She is an affiliate faculty member at the Moore Sloan Data Science Environment at the NYU Center for Data Science, a 2019 Reynolds Journalism Institute Fellow, and her work has been supported by New America, the Institute of Museum & Library Services, and the Tow Center at Columbia Journalism School. Alessio Figalli is the author of Optimal Transportation and Action-Minimizing Measures (0.0 avg rating, 0 ratings, 0 reviews, published 2008), Autour des. Answer (1 of 3): Short answer: yes. Alessio Figalli (talaffuzi: Alessio Figalli) (1984-yil 2-aprelda tugilgan) italiyalik matematik. The other three who won the 2018 Fields Medal are Alessio Figalli from ETH Zurich in Switzerland, who is an Italian; Caucher Birkar from Cambridge, a Kurdish man who came to Britain as a refugee; and Peter Scholze from Bonn University, who is German. Quick on the essential issues, and quick on isolating an important point that is going somehow to yield information for us.. In 2004 Ambrosio took him on as a graduate student and also arranged for him to study under Cdric Villani, a talented mathematician in Lyon, France, who would go on to win the Fields Medal himself a few years later. I like drawing pictures. Finally, he will conclude with a brief description of some results that he recently obtained on the study of ice melting into water. You can read todays latest tweets and post from Alessio Figallis official Twitter account below, where you can know what he is saying in his previous tweet. They realized that whenever you want to compare two shapes which is something mathematicians often want to do you can learn something by thinking about the most efficient, or optimal, way of converting one into the other. [15], invited speaker at the International Congress of Mathematicians, French National Centre for Scientific Research, SISTEMA ETD - Archivio digitale delle tesi discusse presso l'Universit di Pisa, A Traveler Who Finds Stability in the Natural World, August 1, 2018, "Universality in several-matrix models via approximate transport maps", https://en.wikipedia.org/w/index.php?title=Alessio_Figalli&oldid=1133271545, This page was last edited on 13 January 2023, at 00:03. Drop an ice cube into a glass of water. He has also served as an associate professor at the Courant Institute of Mathematical Sciences at New York University. The Fields Medal was awarded for his work studying Partial Differential Equations and the . Consider, again, an ice cube in a glass of water. Figallis first major result as a mathematician had to do with proving the stability of these types of energy-minimizing shapes. Biography [5] He has won the 2015 edition of the Stampacchia Medal, and the 2017 edition of the Feltrinelli Prize for mathematics. Similarly, with crystals, you might ask: If I start with a perfect crystal, then add a small amount of energy by heating it a bit, is the resulting shape similar to the one I started with or dramatically different? It would be adisasterfor the model. He was born in Rome on April 02, 1984. And unlike the paraboloid pattern for the temperature, which implies that a singularity might exist along a whole line, a conical pattern can only have a sharp singularity at a single point. Instead, hes often in England, where his wife, Mikaela Iacobelli, is a mathematician at Durham University. While mathematicians had shown that soap films are always smooth in three dimensions, Almgren proved that in four dimensions, a new kind of branching singularity can appear, making the soap films sharp in strange ways. Since then some . The young Italian mathematician is tall, fit and stylish, his R's rolling off the tongue with an intoxicating Roman richness. You have this sensation of transcendence, you feel like youve been part of something really meaningful.. Complete chaos, said Figalli, who won the Fields Medal, maths highest honor, in 2018. He masters them with a joyful outlook and optimism.
But it has very concrete questions at its origin. document.getElementById("ak_js_1").setAttribute("value",(new Date()).getTime()); Alessio Figalli Educational Qualifications, Antonino Faranda Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family, Ashraf Saber Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family, Crescenzo DAmore Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family, Cristian Lizzori Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family, Alessandro Frau Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Antonino Faranda Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Masahito Yabe Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Matthew Connolly Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Capital Bra Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Corliss Williamson Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023, Jonathan Fumeaux Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family 2023. Alessio Figalli Born (1984-04-02) 2 April 1984(age 38) Rome, Italy Nationality Italian Alma mater University of Pisa Scuola Normale Superiore di Pisa cole normale suprieure de Lyon Spouse(s) Mikaela Iacobelli Awards Prix and Cours Peccot(2012) EMS Prize(2012) Stampacchia Medal(2015) Feltrinelli Prize(2017) Fields Medal(2018) Scientific career Figalli has been on the faculty at ETH Zurich since 2016, when he moved from UT Austin. In the decade before mathematicians began to understand the ice melting equations, they made tremendous progress on the mathematics of soap films. If this was true, it would mean that the singularities in the Stefan problem were completely out of control. What is the physical condition of Alessio Figalli? He has been awarded the Prix and Cours Peccot in 2012, the EMS Prize in 2012,, the Stampacchia Medal in 2015, and the Feltrinelli Prize in 2017. Caffarelli proved singularities exist in the mathematics of melting ice. After all, you do not cut yourself on sharp edges when you pull a piece of ice from a glass of water. Maybe it makes sense to split one wagonload between two destinations. If you dip two wire rings in a soapy solution and then separate them, a soap film forms between them. Prior to the Fields Medal, I had never given a lecture before the general public. Wiki Biography & Celebrity Profiles as wikipedia.
Alessio Figalli - Google Scholar This was his great intuition, said Mingione. When mathematicians zoomed in on solutions to the soap film equations, they saw only flatness. If you move two units away, the temperature rises by approximately four. In 2018 he won the Fields Medal for his contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability. Wife/Spouse: Sarah Paden (Music Teacher) Children: Son- None Daughter(s)- Tara, Tuli: Parents: Father- Venky Venkatesh . The point is, all the properties of the new objects that you want to understand are encoded in the transport, Figalli said. You can find out how much net worth Alessio has this year and how he spent his expenses. Get Quanta Magazine delivered to your inbox. Major events mark turning points: afterwards, much changes.
Alessio Figalli's actual age is 39, and his birthday is on 2-Apr-1984. He likes to be around other people, and other people like to be around him. Continue reading to discover who is Alessio Figalli. But just before that moment, it will form a sheetlike singularity, a two-dimensional wall as sharp as a razor. 276: 2021: Existence and uniqueness of martingale solutions for SDEs . Therefore, anywhere the paraboloid equals zero you have a singularity. Alessio is gaining More popularity of his Profession on Twitter these days. In 2016 he was awarded a European Research Council (ERC) grant, and in 2018 he received the Doctorate Honoris Causa from the Universit Cte dAzur. Mathematics is everywhere. Minimal surfaces appear in many areas of mathematics. Prof. Dr. Alessio Figalli Contact information ETH Zurich Prof. Dr. Alessio Figalli FIM Director Department of Mathematics HG G 45.2 Rmistrasse 101 8092 Zurich Switzerland
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An Invitation to Optimal Transport, Wasserstein Distances, and Gradient He also worked on HamiltonJacobi equations and their connections to weak KolmogorovArnoldMoser theory. He used optimal transport techniques to get improved versions of the anisotropic isoperimetric inequality, and obtained several other important results on the stability of functional and geometric inequalities. To get a sense of it, imagine submerging a thin sheet of ice into water. Alessio Figalli Figalli at Oberwolfach, 2016 Born (1984-04-02) 2 April 1984(age 38) Rome, Italy Nationality Italian Alma mater University of Pisa Scuola Normale Superiore di Pisa cole normale suprieure de Lyon Spouse Mikaela Iacobelli Awards Prix and Cours Peccot(2012) EMS Prize(2012) Stampacchia Medal(2015) Feltrinelli Prize(2017)
Alessio Figalli Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family Do you want to know what is the educational qualifications of Alessio Figalli? In the below table, you will find the height of Alessio Figalli in Meter, Centimeter, and Feet Inche, & the weight in KG and Pound. Man Group plc.
- Wikipedia These singularities are profoundly abstract and impossible to visualize neatly. In Italy, students can enroll in either a classics or a scientific high school.
Fields Medal Alessio Figalli ICM2018__bilibili The Fields Medal has helped to open doors: Its now much easier for me to meet researchers from other disciplines and from the industry.. So what is the networth of Alessio Figalli? We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. Alessio Figalli is an Italian mathematician working primarily on calculus of variations and partial differential equations. He also devised a way of estimating how many there are. 1390 0. Date Written: April 2, 2021. Alessio Figalli(Roma, 2 d'abrilde 1984) s un matemticitaliespecialitzat en equacions en derivades parcials(EDP). 2023 Wiki Biography & Celebrity Profiles as wikipedia, Sun Zhenni Wiki, Biography, Age, Net Worth, Family, Instagram, Twitter, Social Profiles & More Facts, Jodie Fields (Cricketer) Wiki, Biography, Age, Husband, Family, Net Worth, Aleksey Chuklin (Racing Driver) Wiki, Biography, Age, Wife, Family, Net Worth. . In 2019 he received the Doctorate Honoris Causa from the Polytechnic University of Catalonia too. Image: Tatjana Ruf, CC BY-SA 2.0. : Not Known. The same year, Venkatesh wasawarded the J. He was taking on this function at ETH starting on 1 September 2019. This major international event is being organised by the magazine Times Higher Education, which is famous for its ranking. But they found nothing to preclude the model from arriving at scenarios that are improbably weird. Partial Differential Equations (2012) Whilst there is undoubtably an overlap between the skillsets required to participate at a high school math competition and obtaining the Fields Medal, there are a large number (indeed, the majority I believe) of Fields medalists that ha. Over the past few months, hes visited friends in England, where his wife lives, and in Rome, where he grew up. Philipp Ustinov. Quanta Magazine moderates comments tofacilitate an informed, substantive, civil conversation. Crystals are another minimal shape. Since winning the medal, Figalli has been working more closely on topics that concern the development, effects and communication of mathematics. Prof. Alessio Figalli, ETH ZrichSeminar date: January 25, 2022 Talk topic: Optimal transport: past, present, and futureAbstract:At the end of the 18th centu. I always forget about how good he is at math in our normal life, she said. 01 August 2018. But as for the Stefan problem itself, and the mathematics of how ice cubes melt in water? They used Almgrens work to show that the ice around one of these branching singularities must have a conical pattern that looks the same as you keep zooming in.
PDF The Work of Alessio Figalli - International Mathematical Union Alessio Figalli will show some applications of this theory to soap bubbles (isoperimetric inequalities) and clouds (semigeostrophic equations), problems on which he worked over the last 10 years. Mathematics is very important for the current challenges in computer sciences and financial technology, says Figalli.
Alessio Figalli (Author of An Invitation to Optimal Transport He has won the 2015 edition of the Stampacchia Medal, and the 2017 edition of the Feltrinelli Prize for mathematics. 2018-yil Fields medali bilan taqdirlangan.. Figalli 2006-yil Pisa universitetini magistr darajasi bilan tamomlagan. This flatness implied that the geometry near that point could not be singular. 41 (5): 1890-1920 (2009)
One year after the Fields Medal | ETH Zurich Read also: Cristian Lizzori Net Worth, Age, Height, Weight, Wife, Wiki-Bio, Family. He has a wild spectrum of different contributions, said Luis Caffarelli, a mathematician at the University of Texas, Austin, who will introduce Figalli at the Fields Medal ceremony in Rio. The question was whether the two fronts near these points collapsed at the same time. Calculus of Variations Partial Differential Equations. And since they chose the point randomly, they could conclude that all points on the film must look like a smooth plane when you peer at them up close. A mathematician named Frederick Almgren had investigated it in an intimidating 1,000-page paper about soap films, which was only published by his wife, Jean Taylor another expert on soap films after he died. Alessio Figalli2018fields. The same year, he wona Bronze medal in the International Mathematics Olympiad held in Hong Kong. He is seen as one of the most successful Mathematician of all times. Zabv se pedevm varianm potem a parcilnmi diferencilnmi rovnicemi. here to see the students listed in chronological order. Mathematicians have developed formulas and inequalities that are meant to describe what happens when you nudge a soap bubble; theyd like to prove that those mathematical representations feature a degree of stability that matches what we observe in nature. Imagine that you start with a perfect crystal and then deform it slightly through heating. Figalli has a generous helping of each of these, but what stands out most about him is his disposition: He doesnt seem weighed down by mathematics. It was a revelation, he said.
The other three who won the 2018 Fields Medal are Alessio Figalli from ETH Zurich in Switzerland, who is an Italian; Caucher Birkar from Cambridge, a Kurdish man who came to Britain as a refugee; and Peter Scholze from Bonn . Alessio (given name) 1984 births Fields Medalists Winners of Feltrinelli Prize Male mathematicians from Italy Births in Rome Faculty of the ETH Zurich Alumni of the cole Normale Suprieure (Ulm) Alumni of Scuola Normale Superiore Alumni of the University of Pisa Faculty of the University of Texas at Austin Non-topical/index: It wasnt until the 1980s and 1990s that mathematicians began to recognize that optimal transport was a mathematically deep question in its own right and also a tool that they might use to solve other kinds of problems. In physical terms, regularity means that a system evolves in a smooth way. #WorkshopFigalliFME Speakers: Five spanish and catalan mathematicians who have worked (or still working ) with Prof. Alessio Figalli: Xavier Cabr (UPC-ICREA), Xavier Ros-Oton (Universitt Zrich), Joaquim Serra (ETH Zrich), Matteo Bonforte (Universidad Autnoma de . I said: Why not? Usually there are more girls in a classics high school than a scientific high school, so that was another selling point, he said. Anal. Visit the official Facebook, Instagram, Twitter, Wikipedia, and YouTube accounts of Alessio Figalli. Ambrosio expected that the novice student would struggle to get anywhere with it. For instance, youre not limited to transporting soil by the wagonload. In the end, they proved this is in fact how the scenario plays out in the equations. Alessio entered the career as Mathematician In his early life after completing his formal education.. In the 1790s Gaspard Monge had a problem. How tall is Alessio Figalli? Alessio Figalli alla Settimana Matematica 41,634 views Jun 9, 2020 Alessio Figalli, medaglia Fields, incontra gli studenti della scuola in visita al Dipartimento di Matematica. Figalli received his masters degree from the University of Pisa in 2006 (as a student of the Scuola Normale Superiore di Pisa), and earned his doctorate in 2007 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa and Cdric Villani at the cole Normale Suprieure de Lyon. He learned quickly and caught up to his peers within a year. Math. He has this combination of taking a problem that is in principle a natural problem from some other area, and he does his mathematics, and provides a solution., Get highlights of the most important news delivered to your email inbox.
Free boundary regularity in obstacle problems - University of He and his collaborators were at a conference in Edinburgh, where they had been working on the stability problem for many hours a day.