\u00bbThe phase transitions are extremely exciting because we have a very large physical system, i.e. a system that consists of many atoms, but which is also significantly quantum mechanical. We only know quantum mechanics from small things \u2013 atoms, molecules, and so on \u2013 and suddenly we see a much larger physical system that also develops quantum effects,\u00ab he says, and continues:<\/p>\n
\u00bbAs a mathematician, I would like to study the equations and try to understand what mathematical tools we can develop to get a better description of these very peculiar physical systems.\u00ab<\/p>\n
I think very few people know what mathematics actually is before they start at university.<\/p>\n
S\u00f8ren Fournais, Professor of Mathematics, UCPH<\/p>\n<\/blockquote>\n
It does not work by simply \u2018solving’ equations, says S\u00f8ren Fournais. There are many equations that cannot be solved. But this does not mean that we cannot approach a solution, or study the path towards it.<\/p>\n
\u00bbThe Schr\u00f6dinger equation is not just one equation, it covers a large system of thousands of equations \u2013 there is one for an atom, ten atoms, a billion atoms. And the ‘solution’ we have to find will not be a number, but a function that consists of hundreds of thousands of variables.\u00ab<\/p>\n
Striking mathematical beauty<\/h3>\n
Unlike what most people might have learned in primary or secondary school, mathematics \u2013 especially mathematical research \u2013 can be more creative and abstract than logical, according to S\u00f8ren Fournais.<\/p>\n
\u00bbI think very few people know what mathematics actually is before they start at university. At school you learn that mathematics is all about finding a correct answer, but more often it may be more about asking the right questions.\u00ab<\/p>\n
The researcher remembers how surprised he was when he started studying mathematics and physics at the university. A completely new world opened up for him \u2013 and luckily, it turned out that he really thrived in it.<\/p>\n
\u00bbIt was quite different from what I had expected. And I was pleasantly surprised, but it was actually a bit of a coincidence, because I had no prerequisites for knowing what it was I was getting into. That’s why I also have a great understanding for students who start on a study programme and perhaps quickly find out that they have chosen incorrectly.\u00ab<\/p>\n
Hard mathematics is not for everyone, he admits. But those who see and understand its particular nature, find a beauty that can be difficult to convey to the uninitiated.<\/p>\n
\u00bbIt can seem very complicated and abstract. But sometimes you suddenly see it from the right angle, and a simplicity arises that lets you understand incredibly complex things about how the world is interconnected. And this is pretty fantastic,\u00ab says S\u00f8ren Fournais.<\/p>\n
Shower with a Gordian knot<\/h3>\n
However, it is not every day that the beauty breaks out of the shield of complexity in mathematics, according to the professor. He also explains how sometimes you feel trapped within knots that seem impossible to loosen.<\/p>\n
\u00bbWhen you’re working on a mathematical problem for a very long time, as we’re going to be doing here at QMATH in the coming years, it will start sneaking into your thoughts all the time. It will pop up in the evening, just before you go to sleep, while taking a shower, when you take a walk, or when you have a conversation,\u00ab says S\u00f8ren Fournais.<\/p>\n
\u00bbBut then, at some point or other, the many abstract objects will start to take shape inside your head. You will be able to see them separately, and manipulate them until they suddenly fall into place.\u00ab<\/p>\n
This is rarely the case in the stories about the genius, like Newton, who is hit on the head by an apple and gets a brilliant idea, the researcher says.<\/p>\n
\u00bbYou will often solve small knots gradually, typically in conversations and in brainstorming with colleagues. It is therefore also extremely stimulating to be here at QMATH, where so many clever and talented minds are gathered together. I’m so very, very happy to be a part of it,\u00ab says S\u00f8ren Fournais.<\/p>\n
In connection with the large-scale research grant, he moved with his family from Aarhus to Copenhagen to become part of the UCPH Centre for Quantum Mechanics, which, according to him \u00bbis competing with the very best in the world.\u00ab<\/p>\n
Expensive mysteries best solved with chalk<\/h3>\n
Mathematics can be both beautiful and abstract \u2013 but can it also be so expensive that it can cost DKK 15 million to solve an equation?<\/p>\n
\u00bbMathematics is actually a very inexpensive field of research, because we do not need labs or other expensive equipment. We mostly use our computers to write e-mails and manuscripts, because the actual work is mostly on these boards,\u00ab he says, pointing towards a whiteboard that is overwritten with digits and mathematical notation.<\/p>\n
It will pop up in the evening, just before you have to sleep, while taking a shower, when you take a walk, or when you have a conversation<\/p>\n
S\u00f8ren Fournais, Professor of Mathematics, UCPH<\/p>\n<\/blockquote>\n
\u00bbIn fact, we would rather have had ordinary, old-fashioned blackboards with chalk, because it is much easier to work with. As it is now, we often end up getting smeared with marker ink when we stand here writing.\u00ab<\/p>\n
Research funding is therefore almost almost exclusively spent on salaries for the many talented people who will be involved in the project in the coming years, he explains.<\/p>\n
And all these mathematical complexities you are trying to solve… What can they actually be used for in the real world?<\/p>\n
\u00bbI can\u2019t answer. Our job is to learn and create tools that allow us to understand the mathematics of the world better,\u00ab he says, and pauses for reflection.<\/p>\n
\u00bbAnd as a rule, it turns out to be useful when we understand the world a little bit better. But there will be some other researchers who might want to look at what the results can be used for. This is how all basic research works \u2013 we do not know exactly what we will find, but it is usually in this process that the most important research results emerge.\u00ab
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the next few years S\u00f8ren Fournais will be working a good deal with Schr\u00f6dinger's equation, which you can see on the board here."},{"acf_fc_layout":"Standfirst","subject":"Quantum mechanics","text":"Det k\u00f8rer i hovedet hele tiden. N\u00e5r han sover, er v\u00e5gen eller f\u00f8rer en samtale. If\u00f8lge matematikprofessor S\u00f8ren Fournais besidder matematikken en s\u00e6rlig sk\u00f8nhed, som opst\u00e5r, n\u00e5r det abstrakte og helt ubegribeligt komplicerede pludselig bliver simpelt. Nu har han f\u00e5et 15 millioner til at l\u00f8se Schr\u00f6dingers ligning. \r\n\r\nELLER:\r\n\r\nMatematik besidder en s\u00e6rlig sk\u00f8nhed, som opst\u00e5r, n\u00e5r det abstrakte og helt ubegribeligt komplicerede pludselig bliver simpelt, lyder det fra S\u00f8ren Fournais, der har f\u00e5et 15 millioner kroner til at l\u00f8se Schr\u00f6dingers ligning. ","use_post_excerpt":true},{"acf_fc_layout":"Byline","is_author":true,"contributors":false},{"acf_fc_layout":"Content","content":"<p>It describes virtually everything we know.<\/p>\n<p>The Earth we are standing on, the water in the sea, and the stars shining on us from the heavens at night.<\/p>\n<p>The Schr\u00f6dinger equation is one of the fundamental equations of quantum mechanics, and it describes pretty much everything from the atomic to the stellar level. And recently, the UCPH mathematics professor S\u00f8ren Fournais got a staggering DKK 15 million from the European Research Council to solve it.<\/p>\n<p>\u00bbThere are huge things in the universe, galaxies and that kind of stuff, that it does not describe. But apart from that, it is involved in everything we know,\u00ab says the professor of mathematics when we meet him at the UCPH research centre QMATH.<\/p>\n<p>With S\u00f8ren Fournais in charge, a team of researchers, postdocs and PhD students will over the course of the next five years learn more about that part of the equation that deals with the so-called Bose-Einstein condensates, which deals with the cooling of atoms to a phase transition that is neither liquid, fixed, gas or plasma.<\/p>\n<p><strong>READ ALSO:<\/strong><em><a href=\"https:\/\/uniavisen.dk\/en\/danish-scientist-gets-huge-five-year-eu-grant-to-understand-quantum-physics-phenomenon\/\"> Danish scientist gets huge five-year EU grant to understand quantum physics phenomenon<\/a><\/em><\/p>\n<p>\u00bbThe phase transitions are extremely exciting because we have a very large physical system, i.e. a system that consists of many atoms, but which is also significantly quantum mechanical. We only know quantum mechanics from small things \u2013 atoms, molecules, and so on \u2013 and suddenly we see a much larger physical system that also develops quantum effects,\u00ab he says, and continues:<\/p>\n<p>\u00bbAs a mathematician, I would like to study the equations and try to understand what mathematical tools we can develop to get a better description of these very peculiar physical systems.\u00ab<\/p>\n<blockquote><p>I think very few people know what mathematics actually is before they start at university.<\/p>\n<p class=\"quotee\">S\u00f8ren Fournais, Professor of Mathematics, UCPH<\/p>\n<\/blockquote>\n<p>It does not work by simply \u2018solving’ equations, says S\u00f8ren Fournais. There are many equations that cannot be solved. But this does not mean that we cannot approach a solution, or study the path towards it.<\/p>\n<p>\u00bbThe Schr\u00f6dinger equation is not just one equation, it covers a large system of thousands of equations \u2013 there is one for an atom, ten atoms, a billion atoms. And the ‘solution’ we have to find will not be a number, but a function that consists of hundreds of thousands of variables.\u00ab<\/p>\n<h3>Striking mathematical beauty<\/h3>\n<p>Unlike what most people might have learned in primary or secondary school, mathematics \u2013 especially mathematical research \u2013 can be more creative and abstract than logical, according to S\u00f8ren Fournais.<\/p>\n<p>\u00bbI think very few people know what mathematics actually is before they start at university. At school you learn that mathematics is all about finding a correct answer, but more often it may be more about asking the right questions.\u00ab<\/p>\n<p>The researcher remembers how surprised he was when he started studying mathematics and physics at the university. A completely new world opened up for him \u2013 and luckily, it turned out that he really thrived in it.<\/p>\n<p>\u00bbIt was quite different from what I had expected. And I was pleasantly surprised, but it was actually a bit of a coincidence, because I had no prerequisites for knowing what it was I was getting into. That’s why I also have a great understanding for students who start on a study programme and perhaps quickly find out that they have chosen incorrectly.\u00ab<\/p>\n<p>Hard mathematics is not for everyone, he admits. But those who see and understand its particular nature, find a beauty that can be difficult to convey to the uninitiated.<\/p>\n<p>\u00bbIt can seem very complicated and abstract. But sometimes you suddenly see it from the right angle, and a simplicity arises that lets you understand incredibly complex things about how the world is interconnected. And this is pretty fantastic,\u00ab says S\u00f8ren Fournais.<\/p>\n<h3>Shower with a Gordian knot<\/h3>\n<p>However, it is not every day that the beauty breaks out of the shield of complexity in mathematics, according to the professor. He also explains how sometimes you feel trapped within knots that seem impossible to loosen.<\/p>\n<p>\u00bbWhen you’re working on a mathematical problem for a very long time, as we’re going to be doing here at QMATH in the coming years, it will start sneaking into your thoughts all the time. It will pop up in the evening, just before you go to sleep, while taking a shower, when you take a walk, or when you have a conversation,\u00ab says S\u00f8ren Fournais.<\/p>\n<p>\u00bbBut then, at some point or other, the many abstract objects will start to take shape inside your head. You will be able to see them separately, and manipulate them until they suddenly fall into place.\u00ab<\/p>\n<p>This is rarely the case in the stories about the genius, like Newton, who is hit on the head by an apple and gets a brilliant idea, the researcher says.<\/p>\n<p>\u00bbYou will often solve small knots gradually, typically in conversations and in brainstorming with colleagues. It is therefore also extremely stimulating to be here at QMATH, where so many clever and talented minds are gathered together. I’m so very, very happy to be a part of it,\u00ab says S\u00f8ren Fournais.<\/p>\n<p>In connection with the large-scale research grant, he moved with his family from Aarhus to Copenhagen to become part of the UCPH Centre for Quantum Mechanics, which, according to him \u00bbis competing with the very best in the world.\u00ab<\/p>\n<h3>Expensive mysteries best solved with chalk<\/h3>\n<p>Mathematics can be both beautiful and abstract \u2013 but can it also be so expensive that it can cost DKK 15 million to solve an equation?<\/p>\n<p>\u00bbMathematics is actually a very inexpensive field of research, because we do not need labs or other expensive equipment. We mostly use our computers to write e-mails and manuscripts, because the actual work is mostly on these boards,\u00ab he says, pointing towards a whiteboard that is overwritten with digits and mathematical notation.<\/p>\n<blockquote><p>It will pop up in the evening, just before you have to sleep, while taking a shower, when you take a walk, or when you have a conversation<\/p>\n<p class=\"quotee\">S\u00f8ren Fournais, Professor of Mathematics, UCPH<\/p>\n<\/blockquote>\n<p>\u00bbIn fact, we would rather have had ordinary, old-fashioned blackboards with chalk, because it is much easier to work with. As it is now, we often end up getting smeared with marker ink when we stand here writing.\u00ab<\/p>\n<p>Research funding is therefore almost almost exclusively spent on salaries for the many talented people who will be involved in the project in the coming years, he explains.<\/p>\n<p>And all these mathematical complexities you are trying to solve… What can they actually be used for in the real world?<\/p>\n<p>\u00bbI can\u2019t answer. Our job is to learn and create tools that allow us to understand the mathematics of the world better,\u00ab he says, and pauses for reflection.<\/p>\n<p>\u00bbAnd as a rule, it turns out to be useful when we understand the world a little bit better. But there will be some other researchers who might want to look at what the results can be used for. This is how all basic research works \u2013 we do not know exactly what we will find, but it is usually in this process that the most important research results emerge.\u00ab<\/p>\n"},{"acf_fc_layout":"ArticleEnd"},{"acf_fc_layout":"Newsletter","lang_select":"en","identifier":"Newsletter","headline":"Get an email with our top stories","button_text":"Sign up here","class":""},{"acf_fc_layout":"OtherStories","headline":"","hand_picked_posts":true,"references":[{"reference":{"ID":151661,"post_author":"98","post_date":"2023-05-30 07:32:54","post_date_gmt":"2023-05-30 05:32:54","post_content":"S\u00f8ren Fournais (49) is Professor at the Department of Mathematical Sciences and the Centre for the Mathematics of Quantum Theory at the University of Copenhagen. The centre is a world leader in the mathematical understanding of quantum physics, and the work consists partly in finding proofs for already known equations.\r\n\r\n\u00bbA typical week begins with you having some new good ideas from the weekend that you would like to pursue, and then you work hard on Monday, Tuesday and Wednesday. Then it looks like it works, but by Thursday we find out that it does not work anyway. But then you've learned more about it, and then the next round of ideas for the week ahead is perhaps a little bit more validated. And at some point, everything falls into place,\u00ab S\u00f8ren Fournais says in a press release from the University of Copenhagen.\r\n\r\nHe got his PhD From Aarhus University at the age of 26, after which he worked as a postdoc at the Erwin Schr\u00f6dinger Institute in Vienna and at Universit\u00e9 de Paris-Sud, before returning to Aarhus as associate professor and later as professor in 2006. In 2014, he became a member of the Royal Danish Academy of Sciences and Letters, and in 2022 was hired by UCPH.\r\n\r\nOver the past ten years, S\u00f8ren Fournais has investigated the weird characteristics of the so-called Bose-Einstein-condensates - a quantum state where millions of atoms condense and move in concert. This has a certain beauty, according to him, and this is also the reason why you are reading about him now.\n<!-- end of module 1 -->\nWith a grant of DKK 15 million from the European Research Council, S\u00f8ren Fournais will dedicate the next five years to solving the equations of the mystical quantum phenomenon of the Bose-Einstein-condensates:\r\n\r\n\u00bbImagine one of those spectacular opening ceremonies at the Olympic Games, where a huge crowd of people suddenly coerce as a unit, making the same movements synchronously like a flock of starlings. This also happens in the world of atoms under some very particular and extraordinary conditions. Here it is a million atoms, all of which enter into the same quantum state and in this way behave in a completely synchronous manner,\u00ab explains S\u00f8ren Fournais.\r\n\r\nWhen the atoms are cooled to close to absolute zero, the lowest possible temperature of -273,15 \u00b0C, they enter a fifth phase that is neither liquid, solid, gas or plasma.\r\n\r\n\u00bbMy big dream is to mathematically prove the Bose-Einstein-condensation phase transition. But showing the phase transition is extremely difficult, because we take for granted that the particles are moving randomly until the point they stick together. It is very difficult to see why the particles do it and exactly when it will happen,\u00ab says S\u00f8ren Fournais.\r\n\r\nThe funding has been awarded via the highly prestigious <a href=\"https:\/\/erc.europa.eu\/apply-grant\/advanced-grant\">ERC Advanced grants<\/a>, which are awarded to excellent researchers at the top level, and the funds are used to build up a team around a ground-breaking research idea.\n<!-- end of module 2 -->\nS\u00f8ren Fournais got an ERC Starting Grant from the European Research Council in 2008 for the project Mathematical problems in Superconductivity and Bose-Einstein Condensation, and the Independent Research Fund Denmark awarded him a Sapere Aude DFF-Advanced scholarship in the years 2015-2020.\r\n\r\nS\u00f8ren Fournais\u2019 research into Bose-Einstein-condensates has led to some of the world's biggest breakthroughs in the field. He has formulated the proof, for example, of an equation for the basic energy state of a Bose-Einstein-condensate that had been left unproven since approximately 1960.\r\n\r\nIn 2018, the Ministry of Science awarded him the prestigious Eliteforsk award.\n<!-- end of module 3 -->\nYou can read more about the <em><a href=\"https:\/\/www.math.ku.dk\/english\/\">Department of Mathematical Sciences here.<\/a><\/em>\r\n\r\nApart from that, like S\u00f8ren Fournais, you will have to be patient:\r\n\r\n\u00bbI think that it's unrealistic to solve this assignment in five years, but I hope that the project will bring us closer to it than we are today,\u00ab says S\u00f8ren Fournais. \u00bbAnd we still have a lot of sub-targets that we hope to achieve along the way\u00ab.\n<!-- end of module 4 -->\n","post_title":"Danish scientist gets huge five-year EU grant to understand quantum physics phenomenon","post_excerpt":"S\u00f8ren Fournais is one of the world's leading researchers into quantum mechanical equations. Now he has to solve mysteries that no-one has ever been able to solve before.","post_status":"publish","comment_status":"closed","ping_status":"closed","post_password":"","post_name":"danish-scientist-gets-huge-five-year-eu-grant-to-understand-quantum-physics-phenomenon","to_ping":"","pinged":"","post_modified":"2023-06-20 09:06:49","post_modified_gmt":"2023-06-20 07:06:49","post_content_filtered":"","post_parent":0,"guid":"https:\/\/uniavisen.dk\/dansk-forsker-faar-kaempe-bevilling-fra-eu-til-at-forstaa-kvantefysisk-faenomen-paa-fem-aar\/","menu_order":0,"post_type":"post","post_mime_type":"","comment_count":"0","filter":"raw"}}],"category":false,"theme":false,"number_of_posts":"4","style":"default"}]},"taxonomyData":{"category":[{"term_id":46,"name":"Science","slug":"science","term_group":0,"term_taxonomy_id":46,"taxonomy":"category","description":"","parent":0,"count":832,"filter":"raw"}],"post_tag":[{"term_id":6342,"name":"QMATH","slug":"qmath-en","term_group":0,"term_taxonomy_id":6342,"taxonomy":"post_tag","description":"","parent":0,"count":1,"filter":"raw"},{"term_id":6231,"name":"s\u00f8ren fournais","slug":"soeren-fournais-en","term_group":0,"term_taxonomy_id":6231,"taxonomy":"post_tag","description":"","parent":0,"count":2,"filter":"raw"}],"post_format":[],"expression":[{"term_id":14,"name":"Portrait Article","slug":"portrait_article","term_group":0,"term_taxonomy_id":14,"taxonomy":"expression","description":"","parent":0,"count":803,"filter":"raw"}],"translation_priority":[{"term_id":5468,"name":"Optional","slug":"optional-en","term_group":0,"term_taxonomy_id":5468,"taxonomy":"translation_priority","description":"","parent":0,"count":674,"filter":"raw"}]},"featured_media_url":"https:\/\/uniavisen.dk\/wp-content\/uploads\/2023\/06\/dsc_3060-1280x882.jpg","_links":{"self":[{"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/posts\/152685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/users\/99"}],"replies":[{"embeddable":true,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/comments?post=152685"}],"version-history":[{"count":5,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/posts\/152685\/revisions"}],"predecessor-version":[{"id":152734,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/posts\/152685\/revisions\/152734"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/media\/152531"}],"wp:attachment":[{"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/media?parent=152685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/categories?post=152685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uniavisen.dk\/en\/wp-json\/wp\/v2\/tags?post=152685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}