Gábor Tardos is a Hungarian mathematician a professor at Central European University and a Canada Research Chair at Simon Fraser University. He works in combinatorics and computer science, he is the younger brother of Éva Tardos. Tardos started with a result in universal algebra: he exhibited a maximal clone of monotone operations, not finitely generated, he obtained partial results concerning the Hanna Neumann conjecture. With his student, Adam Marcus, he proved a combinatorial conjecture of Zoltán Füredi and Péter Hajnal, known to imply the Stanley–Wilf conjecture. With topological methods he proved that if H is a finite set system consisting of the unions of intervals on two disjoint lines τ ≤ 2 ν holds, where τ is the least number of points covering all elements of H and ν is the size of the largest disjoint subsystem of H. Tardos worked out a method for optimal probabilistic fingerprint codes. Although the mathematical content is hard, the algorithm is easy to implement, he received the European Mathematical Society prize for young researchers at the European Congress of Mathematics in 1992 and the Erdős Prize from the Hungarian Academy of Sciences in 2000.
He received a Lendület Grant from the Hungarian Academy of Sciences. Devised to keep outstanding researchers in Hungary. ———, "Optimal probabilistic fingerprint codes", Journal of the ACM, 55: 116, CiteSeerX 10.1.1.8.8911, doi:10.1145/780542.780561, ISBN 978-1581136746. ———, "Transversals of 2-intervals, a topological approach", Combinatorica, 15: 123–134, doi:10.1007/bf01294464. ———. "On the power of randomization in on-line algorithms", Algorithmica, 11: 2–14, doi:10.1007/bf01294260. ———, "A maximal clone of monotone operations, not finitely generated", Order, 3: 211–218, doi:10.1007/bf00400284. Gábor Tardos at the Mathematics Genealogy Project
Loïc Merel is a French mathematician. His research interests include number theory. Born in Carhaix-Plouguer, Merel became a student at the École Normale Supérieure, he finished his doctorate at Pierre and Marie Curie University under supervision of Joseph Oesterlé in 1993. His thesis on modular symbols took inspiration from the work of Yuri Manin and Barry Mazur from the 1970s. In 1996, Merel proved the torsion conjecture for elliptic curves over any number field. Merel has received numerous awards, including the EMS Prize, the Blumenthal Award for the advancement of research in pure mathematics, the Grand Prix Jacques Herbrand of the French Academy of Sciences. Website at Paris Diderot University
Europe is a continent located in the Northern Hemisphere and in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west and the Mediterranean Sea to the south, it comprises the westernmost part of Eurasia. Since around 1850, Europe is most considered to be separated from Asia by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas and the waterways of the Turkish Straits. Although the term "continent" implies physical geography, the land border is somewhat arbitrary and has been redefined several times since its first conception in classical antiquity; the division of Eurasia into two continents reflects East-West cultural and ethnic differences which vary on a spectrum rather than with a sharp dividing line. The geographic border does not follow political boundaries, with Turkey and Kazakhstan being transcontinental countries. A strict application of the Caucasus Mountains boundary places two comparatively small countries and Georgia, in both continents.
Europe covers 2 % of the Earth's surface. Politically, Europe is divided into about fifty sovereign states of which the Russian Federation is the largest and most populous, spanning 39% of the continent and comprising 15% of its population. Europe had a total population of about 741 million as of 2016; the European climate is affected by warm Atlantic currents that temper winters and summers on much of the continent at latitudes along which the climate in Asia and North America is severe. Further from the sea, seasonal differences are more noticeable than close to the coast. Europe, in particular ancient Greece, was the birthplace of Western civilization; the fall of the Western Roman Empire in 476 AD and the subsequent Migration Period marked the end of ancient history and the beginning of the Middle Ages. Renaissance humanism, exploration and science led to the modern era. Since the Age of Discovery started by Portugal and Spain, Europe played a predominant role in global affairs. Between the 16th and 20th centuries, European powers controlled at various times the Americas all of Africa and Oceania and the majority of Asia.
The Age of Enlightenment, the subsequent French Revolution and the Napoleonic Wars shaped the continent culturally and economically from the end of the 17th century until the first half of the 19th century. The Industrial Revolution, which began in Great Britain at the end of the 18th century, gave rise to radical economic and social change in Western Europe and the wider world. Both world wars took place for the most part in Europe, contributing to a decline in Western European dominance in world affairs by the mid-20th century as the Soviet Union and the United States took prominence. During the Cold War, Europe was divided along the Iron Curtain between NATO in the West and the Warsaw Pact in the East, until the revolutions of 1989 and fall of the Berlin Wall. In 1949 the Council of Europe was founded, following a speech by Sir Winston Churchill, with the idea of unifying Europe to achieve common goals, it includes all European states except for Belarus and Vatican City. Further European integration by some states led to the formation of the European Union, a separate political entity that lies between a confederation and a federation.
The EU originated in Western Europe but has been expanding eastward since the fall of the Soviet Union in 1991. The currency of most countries of the European Union, the euro, is the most used among Europeans. In classical Greek mythology, Europa was a Phoenician princess; the word Europe is derived from her name. The name contains the elements εὐρύς, "wide, broad" and ὤψ "eye, countenance", hence their composite Eurṓpē would mean "wide-gazing" or "broad of aspect". Broad has been an epithet of Earth herself in the reconstructed Proto-Indo-European religion and the poetry devoted to it. There have been attempts to connect Eurṓpē to a Semitic term for "west", this being either Akkadian erebu meaning "to go down, set" or Phoenician'ereb "evening, west", at the origin of Arabic Maghreb and Hebrew ma'arav. Michael A. Barry, professor in Princeton University's Near Eastern Studies Department, finds the mention of the word Ereb on an Assyrian stele with the meaning of "night, sunset", in opposition to Asu " sunrise", i.e. Asia.
The same naming motive according to "cartographic convention" appears in Greek Ἀνατολή. Martin Litchfield West stated that "phonologically, the match between Europa's name and any form of the Semitic word is poor." Next to these hypotheses there is a Proto-Indo-European root *h1regʷos, meaning "darkness", which produced Greek Erebus. Most major world languages use words derived from Europa to refer to the continent. Chinese, for example, uses the word Ōuzhōu. In some Turkic languages the Persian name Frangistan is used casually in referring to much of Europe, besides official names such as Avrupa or Evropa; the prevalent definition of Europe as a geographical term has been in use since the mid-19th century. Europe is taken to be bounded by large bodies of water
Helsinki is the capital and most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of Uusimaa in southern Finland, has a population of 650,058; the city's urban area has a population of 1,268,296, making it by far the most populous urban area in Finland as well as the country's most important center for politics, finance and research. Helsinki is located 80 kilometres north of Tallinn, Estonia, 400 km east of Stockholm, 390 km west of Saint Petersburg, Russia, it has close historical ties with these three cities. Together with the cities of Espoo and Kauniainen, surrounding commuter towns, Helsinki forms the Greater Helsinki metropolitan area, which has a population of nearly 1.5 million. Considered to be Finland's only metropolis, it is the world's northernmost metro area with over one million people as well as the northernmost capital of an EU member state. After Stockholm and Oslo, Helsinki is the third largest municipality in the Nordic countries.
The city is served by the international Helsinki Airport, located in the neighboring city of Vantaa, with frequent service to many destinations in Europe and Asia. Helsinki was the World Design Capital for 2012, the venue for the 1952 Summer Olympics, the host of the 52nd Eurovision Song Contest. Helsinki has one of the highest urban standards of living in the world. In 2011, the British magazine Monocle ranked Helsinki the world's most liveable city in its liveable cities index. In the Economist Intelligence Unit's 2016 liveability survey, Helsinki was ranked ninth among 140 cities. According to a theory presented in the 1630s, settlers from Hälsingland in central Sweden had arrived to what is now known as the Vantaa River and called it Helsingå, which gave rise to the names of Helsinge village and church in the 1300s; this theory is questionable, because dialect research suggests that the settlers arrived from Uppland and nearby areas. Others have proposed the name as having been derived from the Swedish word helsing, an archaic form of the word hals, referring to the narrowest part of a river, the rapids.
Other Scandinavian cities at similar geographic locations were given similar names at the time, e.g. Helsingør in Denmark and Helsingborg in Sweden; when a town was founded in Forsby village in 1548, it was named Helsinge fors, "Helsinge rapids". The name refers to the Vanhankaupunginkoski rapids at the mouth of the river; the town was known as Helsinge or Helsing, from which the contemporary Finnish name arose. Official Finnish Government documents and Finnish language newspapers have used the name Helsinki since 1819, when the Senate of Finland moved itself into the city from Turku; the decrees issued in Helsinki were dated with Helsinki as the place of issue. This is; as part of the Grand Duchy of Finland in the Russian Empire, Helsinki was known as Gelsingfors in Russian. In Helsinki slang, the city is called Stadi. Hesa, is not used by natives of the city. Helsset is the Northern Sami name of Helsinki. In the Iron Age the area occupied by present day Helsinki was inhabited by Tavastians, they used the area for fishing and hunting, but due to a lack of archeological finds it is difficult to say how extensive their settlements were.
Pollen analysis has shown that there were cultivating settlements in the area in the 10th century and surviving historical records from the 14th century describe Tavastian settlements in the area. Swedes colonized the coastline of the Helsinki region in the late 13th century after the successful Second Crusade to Finland, which led to the defeat of the Tavastians. Helsinki was established as a trading town by King Gustav I of Sweden in 1550 as the town of Helsingfors, which he intended to be a rival to the Hanseatic city of Reval. In order to populate his newly founded town, the King issued an order to resettle the bourgeoisie of Porvoo, Ekenäs, Rauma and Ulvila into the town. Little came of the plans as Helsinki remained a tiny town plagued by poverty and diseases; the plague of 1710 killed the greater part of the inhabitants of Helsinki. The construction of the naval fortress Sveaborg in the 18th century helped improve Helsinki's status, but it was not until Russia defeated Sweden in the Finnish War and annexed Finland as the autonomous Grand Duchy of Finland in 1809 that the town began to develop into a substantial city.
Russians besieged the Sveaborg fortress during the war, about one quarter of the town was destroyed in an 1808 fire. Russian Emperor Alexander I of Russia moved the Finnish capital from Turku to Helsinki in 1812 to reduce Swedish influence in Finland, to bring the capital closer to Saint Petersburg. Following the Great Fire of Turku in 1827, the Royal Academy of Turku, which at the time was the country's only university, was relocated to Helsinki and became the modern University of Helsinki; the move helped set it on a path of continuous growth. This transformation is apparent in the downtown core, rebuilt in the neoclassical style to resemble Saint Petersburg to a plan by the German-born architect C. L. Engel; as elsewhere, technological advancements such as railroads and industrialization were key factors behind the city's growth. Despite the tumultuous nature of Finnish history during the first half of the 20th century, Helsinki continued its steady development. A landmark e
Stefan Müller (mathematician)
Stefan Müller is a German mathematician and a professor at the University of Bonn. He has been one of the founding directors of the Max Planck Institute for Mathematics in the Sciences in 1996 and was acting there until 2008, he is well known for the calculus of variations. He is interested in the application of mathematical methods in the theory continuum mechanics material science and problems involving microstructures. 1992 - EMS Prize 1993 – Max-Planck-Forschungspreis, together Vladimir Sverák 1999 – CICIAM Collatz Prize ICIAM Edinburgh 2000 – Gottfried Wilhelm Leibniz Prize 2006 – Keith Medal of the Royal Society of Edinburgh and Gauss Lectureship of the German Mathematical Society. Microstructures, phase transitions and geometry. In: Balog: Proceedings European Congress of Mathematicians. Volume 2, Birkhäuser 1998, S.92. with Sverak: Unexpected solutions of first and second order partial differential equations. International Congress of Mathematicians, 1998, Bd. II, S.691, Documenta Mathematica.
With Bethuel, Steffen: Variational models for microstructure and phase transitions. In: Hildebrandt, Struwe: Calculus of Variations and geometric evolution problems. Lecture Notes in Mathematics, volume 1713, 1999, S.85-210. Mathematik und intelligente Materialien. In: Aigner, Behrends: Alles Mathematik. Vieweg 2002. Mathematik ist überall. DMV-Mitteilungen, Januar 1998. Mit Conti, DeSimone, Dolzmann, F. Otto: Multiscale modeling of materials – the role of analysis. In: Kirkilionis, Krömker, Tomi: Trends in Nonlinear Analysis. Springer 2003, S.375-408. G. Friesecke, R. D. James, S. Müller: A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Rat. Mech. Anal. Volume 180, 2006, S. 183-236. C. De Lellis, S. Müller: Sharp rigidity estimates for nearly umbilical surfaces. J. Differential Geometry volume 69, 2005, S. 75-110. S. Müller, V. Sverak: Convex integration for Lipschitz mappings and counterexamples to regularity. Ann. Math. Volume 157, 2003, 715-742. G. Friesecke, R. D. James, S. Müller: A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity.
Comm. Pure Appl. Math. Volume 55, 2002, 1461-1506. A. De Simone, R. V. Kohn, S. Müller, F. Otto: A reduced theory for thin-film micromagnetics. Comm. Pure Appl. Math. Volume 55, 2002, 1408-1460. Müllers Homepage at MPI MIS
Friedrich Ernst Peter Hirzebruch ForMemRS was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, a leading figure in his generation. He has been described as "the most important mathematician in Germany of the postwar period." Hirzebruch was born in Hamm, Westphalia in 1927. His father of the same name was a math teacher. Hirzebruch studied at the University of Münster from 1945–1950, with one year at ETH Zürich. Hirzebruch held a position at Erlangen, followed by the years 1952–54 at the Institute for Advanced Study in Princeton, New Jersey. After one year at Princeton University 1955–56, he was made a professor at the University of Bonn, where he remained, becoming director of the Max-Planck-Institut für Mathematik in 1981. More than 300 people gathered in celebration of his 80th birthday in Bonn in 2007; the Hirzebruch–Riemann–Roch theorem for complex manifolds was a major advance and became part of the mainstream developments around the classical Riemann–Roch theorem.
Hirzebruch's book Neue topologische Methoden in der algebraischen Geometrie was a basic text for the'new methods' of sheaf theory, in complex algebraic geometry. He went on to write the foundational papers on topological K-theory with Michael Atiyah, collaborate with Armand Borel on the theory of characteristic classes. In his work he provided a detailed theory of Hilbert modular surfaces, working with Don Zagier. In March 1945, Hirzebruch became a soldier, in April, in the last weeks of Hitler's rule, he was taken prisoner by the British forces invading Germany from the west; when a British soldier found that he was studying mathematics, he drove him home and released him, told him to continue studying. Hirzebruch died at the age of 84 on 27 May 2012. Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989; the government of Japan awarded him the Order of the Sacred Treasure in 1996. Hirzebruch won an Einstein Medal in 1999, received the Cantor medal in 2004.
Hirzebruch was a foreign member of numerous academies and societies, including the United States National Academy of Sciences, the Russian Academy of Sciences, the Royal Society and the French Academy of Sciences. In 1980–81 he delivered the first Sackler Distinguished Lecture in Israel
Warsaw is the capital and largest city of Poland. The metropolis stands on the Vistula River in east-central Poland and its population is estimated at 1.770 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 8th most-populous capital city in the European Union. The city limits cover 516.9 square kilometres, while the metropolitan area covers 6,100.43 square kilometres. Warsaw is an alpha global city, a major international tourist destination, a significant cultural and economic hub, its historical Old Town was designated a UNESCO World Heritage Site. Once described as the'Paris of the North', Warsaw was believed to be one of the most beautiful cities in the world until World War II. Bombed at the start of the German invasion in 1939, the city withstood a siege for which it was awarded Poland's highest military decoration for heroism, the Virtuti Militari. Deportations of the Jewish population to concentration camps led to the Warsaw Ghetto Uprising in 1943 and the destruction of the Ghetto after a month of combat.
A general Warsaw Uprising between August and October 1944 led to greater devastation and systematic razing by the Germans in advance of the Vistula–Oder Offensive. Warsaw gained the new title of Phoenix City because of its extensive history and complete reconstruction after World War II, which had left over 85% of its buildings in ruins. Warsaw is one of Europe's most dynamic metropolitan cities. In 2012 the Economist Intelligence Unit ranked Warsaw as the 32nd most liveable city in the world. In 2017 the city came 4th in the "Business-friendly" category and 8th in "Human capital and life style", it was ranked as one of the most liveable cities in Central and Eastern Europe. The city is a significant centre of research and development, Business process outsourcing, Information technology outsourcing, as well as of the Polish media industry; the Warsaw Stock Exchange is most important in Central and Eastern Europe. Frontex, the European Union agency for external border security as well as ODIHR, one of the principal institutions of the Organization for Security and Cooperation in Europe have their headquarters in Warsaw.
Together with Frankfurt and Paris, Warsaw is one of the cities with the highest number of skyscrapers in the European Union. The city is the seat of the Polish Academy of Sciences, Warsaw National Philharmonic Orchestra, University of Warsaw, the Warsaw Polytechnic, the National Museum, the Great Theatre—National Opera, the largest of its kind in the world, the Zachęta National Gallery of Art; the picturesque Old Town of Warsaw, which represents examples of nearly every European architectural style and historical period, was listed as a World Heritage Site by UNESCO in 1980. Other main architectural attractions include the Castle Square with the Royal Castle and the iconic King Sigismund's Column, the Wilanów Palace, the Łazienki Palace, St. John's Cathedral, Main Market Square, palaces and mansions all displaying a richness of colour and detail. Warsaw is positioning itself as Central and Eastern Europe’s chic cultural capital with thriving art and club scenes and serious restaurants, with around a quarter of the city's area occupied by parks.
Warsaw's name in the Polish language is Warszawa. Other previous spellings of the name may have included Werszewa. According to some sources, the origin of the name is unknown. In Pre-Slavic toponomastic layer of Northern Mazovia: corrections and addenda, it is stated that the toponymy of northern Mazovia tends to have unclear etymology. Warszawa was the name of a fishing village. According to one theory Warszawa means "belonging to Warsz", Warsz being a shortened form of the masculine name of Slavic origin Warcisław; however the ending -awa is unusual for a big city. Folk etymology attributes the city name to a fisherman and his wife, Sawa. According to legend, Sawa was a mermaid living in the Vistula River. In actuality, Warsz was a 12th/13th-century nobleman who owned a village located at the modern-day site of the Mariensztat neighbourhood. See the Vršovci family which had escaped to Poland; the official city name in full is miasto stołeczne Warszawa. A native or resident of Warsaw is known as a Varsovian – in Polish warszawiak, warszawianka and warszawianie.
Other names for Warsaw include Varsovia and Varsóvia, Varsavia, Warschau, װאַרשע /Varshe, Varšuva, Varsó and Varšava The first fortified settlements on the site of today's Warsaw were located in Bródno and Jazdów. After Jazdów was raided by nearby clans and dukes, a new similar settlement was established on the site of a small fishing village called Warszowa; the Prince of Płock, Bolesław II of Masovia, established this settlement, the modern-day Warsaw, in about 1300. In the beginning of the 14th century it became one of the seats of the Dukes of Masovia, becoming the official capital of the Masovian Duchy in 1413. 14th-century Warsaw's economy rested on crafts and trade. Upon the extinction of the local ducal line, the duchy was reincorporated into the Crown of the Kingdom of Poland in 1526. In 1529, Warsaw for the first time became the seat of th