The best part of being a professor is the opportunity to collaborating with brilliant minds who are excited to do original work. That said, graduate study and postdoctoral research are substantial commitments for both the mentors and mentees. Decisions about joining the group should be made as rationally and transparently as possible. To help potential candidates determine whether my research group is right for you, I have provided my thought and some data about my research group ,which candidates can be used to evaluate whether my research group is a good fit. As such, this page is not for providing generalizable advice, but merely a description of the operation of the research group such that informed decisions can be made.
Job Placement of graduated team members
Since joining Columbia in 2014, I have graduated 10 Ph.D. students. They have been all supported by external grants from the US government. Five of them found tenure track positions - Northwestern (BB), Case Western (HSS), McMaster (SHN, now Inha University, Korea), Northeastern (YL) and Rutgers (NNV) ). Two graduate (EB, KW, JP) joined Los Alamos National Laboratory as postdoctoral research associates and subsequently transitioned to research scientist positions in Los Alamos and Exxonmobil. Other graduates have pursued successful careers in industry upon graduation. The complete list of PhD graduates from my research group can be found in the Mathematics Genealogy [URL]. Five of my former postdocs are now associate or full professors at Seoul National University and the Chinese Academy of Sciences and Southeast University in China and Rowan University (see specific job placements in the team member page [URL]), and University of Kassel in Germany.
Since joining Columbia in 2014, I have graduated 10 Ph.D. students. They have been all supported by external grants from the US government. Five of them found tenure track positions - Northwestern (BB), Case Western (HSS), McMaster (SHN, now Inha University, Korea), Northeastern (YL) and Rutgers (NNV) ). Two graduate (EB, KW, JP) joined Los Alamos National Laboratory as postdoctoral research associates and subsequently transitioned to research scientist positions in Los Alamos and Exxonmobil. Other graduates have pursued successful careers in industry upon graduation. The complete list of PhD graduates from my research group can be found in the Mathematics Genealogy [URL]. Five of my former postdocs are now associate or full professors at Seoul National University and the Chinese Academy of Sciences and Southeast University in China and Rowan University (see specific job placements in the team member page [URL]), and University of Kassel in Germany.
General Recruitment Plan
The recruitment depends on the funding availability, time constraints, and my ability to maintain research quality for existing group members. My goal is to seek team members with a highly chance of conducting interesting and important research. I seek students who are most likely to thrive in the environment and resource I can provide, based on the evidence presented to me. There are excellent students and researchers who are not compatible with the research group. As such, a rejection is not necessarily a reflection of the quality of the candidates.
The recruitment depends on the funding availability, time constraints, and my ability to maintain research quality for existing group members. My goal is to seek team members with a highly chance of conducting interesting and important research. I seek students who are most likely to thrive in the environment and resource I can provide, based on the evidence presented to me. There are excellent students and researchers who are not compatible with the research group. As such, a rejection is not necessarily a reflection of the quality of the candidates.
Postdoc Research scientist/Associate Research Scientist/Research Scientist
Postdoc candidates are recruited based on (1) future potential, and (2) compatibility. Typically, I will only have at most one associate research scientist or research scientist in my research group, served as the deputy group leader when needed. The appointment of such position requires the approval of the department. The position is supported by external funding from research projects and carried the officer rank at Columbia but is generally not open to fresh PhD graduate. The salary and benefit data can be found at the website of the Provost's office. Postdoctoral and associate research scientists are unionized.
Postdoc candidates are recruited based on (1) future potential, and (2) compatibility. Typically, I will only have at most one associate research scientist or research scientist in my research group, served as the deputy group leader when needed. The appointment of such position requires the approval of the department. The position is supported by external funding from research projects and carried the officer rank at Columbia but is generally not open to fresh PhD graduate. The salary and benefit data can be found at the website of the Provost's office. Postdoctoral and associate research scientists are unionized.
Logistics of Ph.D. applications
Interested candidates please contact me and visit http://gradengineering.columbia.edu/onlineapplication for general information. Answers to general admission questions can be found at http://gradengineering.columbia.edu/frequently-asked-questions-2. In your application, please indicate your interest to work with my research group. I also highly recommend students applying for the NSF Graduate Fellowship, the DOE Office of Science Graduate Fellowship, the Marie Curie International Outgoing Fellowship, and the NDSEG Fellowship. Please notice that my Columbia email account will filter out the generic application emails sent to numerous recipients/universities and classified them as spams. Please be specific about (1) why you think our research group is a good fit for you and (2) why you want to attend graduate school.
The PhD application process begins in the Fall semester each year. The review of the Ph.D. applications typically begins in the spring and ends before the summer. Ideally, the successful Ph.D. candidates should have (1) a master degree in civil engineering, applied mechanics, mechanical engineering, applied mathematics, or any other related disciplines, (2) some background in computational mechanics and reasonable mathematical skills (e.g. linear algebra (the understanding of a space, e.g. orthogonality, dimensionality, basis) , undergraduate calculus (the ability to express how things changes with respect to other factors), ordinary/partial differential equations (the ability to predict evolutions), (3) be proficient in Python and C++ code developments (the ability to convert your ideas into program), and (4) possess excellent communication skills (the ability to express the outcomes efficiently).
In the past, the maximum team members I recruited in one single year is 3, the lowest is 0. My hope is to have the students graduate as soon as there is a plausible chance for the student to land a great position. Ph.D. students in my group on average takes four years to finish their Ph.D if they have a master's degree in a related field. All of my current and former PhD students in my research group have been fully funded during the entire period they work with me. Typically, students are supported by a combination of fellowships (Fulbright, NDSEG, Presidential fellowship), research assistantship from research grant and teaching assistant support. Ideally, each PhD student should serve at least once as TA to get some teaching experience (especially if they are interested at academic position) within the first 2 years of PhD study and then support the last two years of all of my PhD students' work with RA or fellowship, if such a support is provided by the department.
Admitted SEAS master students with sufficient background in computational mechanics and/or geomechanics are invited to schedule appointments to discuss possible Ph.D./MS projects with me ([email protected]). For Columbia MS students interested to work with me for PhD, taking the Computational Poromechanics course (ENME6320) or Finite Element in Geotechnical Engineering (now Computational Mechanics with AI) (CIENE4263) offered during the Autumn semester is necessary.
Interested candidates please contact me and visit http://gradengineering.columbia.edu/onlineapplication for general information. Answers to general admission questions can be found at http://gradengineering.columbia.edu/frequently-asked-questions-2. In your application, please indicate your interest to work with my research group. I also highly recommend students applying for the NSF Graduate Fellowship, the DOE Office of Science Graduate Fellowship, the Marie Curie International Outgoing Fellowship, and the NDSEG Fellowship. Please notice that my Columbia email account will filter out the generic application emails sent to numerous recipients/universities and classified them as spams. Please be specific about (1) why you think our research group is a good fit for you and (2) why you want to attend graduate school.
The PhD application process begins in the Fall semester each year. The review of the Ph.D. applications typically begins in the spring and ends before the summer. Ideally, the successful Ph.D. candidates should have (1) a master degree in civil engineering, applied mechanics, mechanical engineering, applied mathematics, or any other related disciplines, (2) some background in computational mechanics and reasonable mathematical skills (e.g. linear algebra (the understanding of a space, e.g. orthogonality, dimensionality, basis) , undergraduate calculus (the ability to express how things changes with respect to other factors), ordinary/partial differential equations (the ability to predict evolutions), (3) be proficient in Python and C++ code developments (the ability to convert your ideas into program), and (4) possess excellent communication skills (the ability to express the outcomes efficiently).
In the past, the maximum team members I recruited in one single year is 3, the lowest is 0. My hope is to have the students graduate as soon as there is a plausible chance for the student to land a great position. Ph.D. students in my group on average takes four years to finish their Ph.D if they have a master's degree in a related field. All of my current and former PhD students in my research group have been fully funded during the entire period they work with me. Typically, students are supported by a combination of fellowships (Fulbright, NDSEG, Presidential fellowship), research assistantship from research grant and teaching assistant support. Ideally, each PhD student should serve at least once as TA to get some teaching experience (especially if they are interested at academic position) within the first 2 years of PhD study and then support the last two years of all of my PhD students' work with RA or fellowship, if such a support is provided by the department.
Admitted SEAS master students with sufficient background in computational mechanics and/or geomechanics are invited to schedule appointments to discuss possible Ph.D./MS projects with me ([email protected]). For Columbia MS students interested to work with me for PhD, taking the Computational Poromechanics course (ENME6320) or Finite Element in Geotechnical Engineering (now Computational Mechanics with AI) (CIENE4263) offered during the Autumn semester is necessary.
Financial Support
The 2024-2025 PhD student in appointment is $48,080 for 12 months or $42,425 for 9-month. For students in their funded years, the University covers the Facilities fee, Columbia Health & Related Services Fee, ISSO fee for international students, upgraded printing fee, and gym access fee. In addition, full tuition remission (e.g., for a first-year PhD student, $55,184 for 2024-2025) for students are provided in their funded years. In addition, the student also received guaranteed university housing for 5 years, medical coverage and $5,500 child care benefit for each child under the age of 6. In addition, the university has also established a Health Funds in which student can apply for support. See the Columbia official website for updated information. For information about housing options for graduate students, please visit http://engineering.columbia.edu/housing-2.
The 2024-2025 PhD student in appointment is $48,080 for 12 months or $42,425 for 9-month. For students in their funded years, the University covers the Facilities fee, Columbia Health & Related Services Fee, ISSO fee for international students, upgraded printing fee, and gym access fee. In addition, full tuition remission (e.g., for a first-year PhD student, $55,184 for 2024-2025) for students are provided in their funded years. In addition, the student also received guaranteed university housing for 5 years, medical coverage and $5,500 child care benefit for each child under the age of 6. In addition, the university has also established a Health Funds in which student can apply for support. See the Columbia official website for updated information. For information about housing options for graduate students, please visit http://engineering.columbia.edu/housing-2.
Research approaches
A professor has many responsibilities. In particular, a successful professor must be a capable researcher, scholar, educator, and principal investigator (PI) who serves the universities/laboratories that provide employments, the research communities that evaluate merits, and the funding agencies that provide sustainability of the research group. In general, fulfilling one of these responsibilities often support the mission of the others, but this is not always the case. What I consider below is solely about the role of PI. In particular, I am consider how the PI's decisions and the subsequent collaborations (of which the support of the team members and collaborators is critical) affect the research group.
The PI's primary role, in my humble opinion, is to direct the research group to conduct research that have long-lasting impacts . The harder the research to be replaced, the more competitive the graduates of the research group can thrive in a job market. This is particularly true for the students capable of developing skills that are in high demand and short supply. Unfortunately, research activities with expectable rewards are often routine (e.g., reimplementing a high-performance finite element code in a new language) or incremental (e.g., proposing modifications of existing models for a set of purposes that are on demands ). While incremental research could be important , they are more suitable for industry and government laboratories with closer ties to the applications that ensure impacts.
In research, the trade-off of this high reward is risk of wasting time. In a competitive ecosystem where any edge will soon be discovered and hence depreciate, transformative research often requires exposure to risk. The outcomes are expected uncertain and rewards are uneven. There are a few effective tools I found useful to manage the risk, i.e., to make swift decisions, limit the exposure (by converting research ideas into pre-prints and publication fast) and/adapt the scope of the research plan to the current situations. A key challenge of management is to precisely place the suitable ideas and workload to the team members and myself such that the research activities can maximize the opportunities to succeed, while enabling the correct portion of low-hanging fruit research for practical reasons (see Tao's essay). This distribution of ideas and workloads are adjusted periodically based on the assessment of the performance of each team members and other relevant evidence gather from my observations.
Every project has two pillars: idea generation and execution. A weak idea executed flawlessly wastes effort; a strong idea executed poorly squanders opportunity. Both skills improve with practice, but the PI’s most effective role is to guide and share experience, not to script every step. To sharpen ideas, students should read widely and deeply, attend high-quality seminars and conferences, and cultivate taste in the subject. Cross-pollination—from other fields and from curiosity-driven detours—often elevates idea quality. Sometimes it is important to let curiosity wander. Execution, in turn, demands knowledge, discipline, logistical planning and, in larger project, coordination and effective communications. Ideally, brainstorming culminates in a concrete plan that is then carried out. In reality, ideation and execution are intertwined and iterative; new evidence or opportunities may require revisiting assumptions and updating the plan that balances originality with pragmatism and speed with rigor.
A professor has many responsibilities. In particular, a successful professor must be a capable researcher, scholar, educator, and principal investigator (PI) who serves the universities/laboratories that provide employments, the research communities that evaluate merits, and the funding agencies that provide sustainability of the research group. In general, fulfilling one of these responsibilities often support the mission of the others, but this is not always the case. What I consider below is solely about the role of PI. In particular, I am consider how the PI's decisions and the subsequent collaborations (of which the support of the team members and collaborators is critical) affect the research group.
The PI's primary role, in my humble opinion, is to direct the research group to conduct research that have long-lasting impacts . The harder the research to be replaced, the more competitive the graduates of the research group can thrive in a job market. This is particularly true for the students capable of developing skills that are in high demand and short supply. Unfortunately, research activities with expectable rewards are often routine (e.g., reimplementing a high-performance finite element code in a new language) or incremental (e.g., proposing modifications of existing models for a set of purposes that are on demands ). While incremental research could be important , they are more suitable for industry and government laboratories with closer ties to the applications that ensure impacts.
In research, the trade-off of this high reward is risk of wasting time. In a competitive ecosystem where any edge will soon be discovered and hence depreciate, transformative research often requires exposure to risk. The outcomes are expected uncertain and rewards are uneven. There are a few effective tools I found useful to manage the risk, i.e., to make swift decisions, limit the exposure (by converting research ideas into pre-prints and publication fast) and/adapt the scope of the research plan to the current situations. A key challenge of management is to precisely place the suitable ideas and workload to the team members and myself such that the research activities can maximize the opportunities to succeed, while enabling the correct portion of low-hanging fruit research for practical reasons (see Tao's essay). This distribution of ideas and workloads are adjusted periodically based on the assessment of the performance of each team members and other relevant evidence gather from my observations.
Every project has two pillars: idea generation and execution. A weak idea executed flawlessly wastes effort; a strong idea executed poorly squanders opportunity. Both skills improve with practice, but the PI’s most effective role is to guide and share experience, not to script every step. To sharpen ideas, students should read widely and deeply, attend high-quality seminars and conferences, and cultivate taste in the subject. Cross-pollination—from other fields and from curiosity-driven detours—often elevates idea quality. Sometimes it is important to let curiosity wander. Execution, in turn, demands knowledge, discipline, logistical planning and, in larger project, coordination and effective communications. Ideally, brainstorming culminates in a concrete plan that is then carried out. In reality, ideation and execution are intertwined and iterative; new evidence or opportunities may require revisiting assumptions and updating the plan that balances originality with pragmatism and speed with rigor.
Expectations on students and postdoc associates
I expect that all Ph.D. students and postdoc research scientists will produce research results worthy of publishing in well-respected peer-reviewed journals within a reasonable amount of time in my research group (e.g. Computer Methods in Applied Mechanics and Engineering [PDF1][PDF2][PDF3][URL], Journal of Engineering Mechanics [PDF], International Journal for Numerical Methods in Engineering [PDF] and International Journal of Analytical and Numerical Methods in Geomechanics [PDF]). Co-authoring a manuscript can provide valuable insights on the quality of the collaborations for both the PI and the students. This knowledge can help adjusting the strategies to ensure successful mentorship. All group members, including myself, must uphold the highest standards of rigor and integrity. I encourage everyone to plan research activities by balancing risk and reward. Often, groundbreaking work requires stepping away from conventional approaches; however, there is no value in novelty for its own sake. What often distinguishes excellent researchers from good ones is the ability to calculate and manage risk, devise plans, and execute them so that the chances of asking the right questions — and finding correct answers — are maximized.
I expect that all Ph.D. students and postdoc research scientists will produce research results worthy of publishing in well-respected peer-reviewed journals within a reasonable amount of time in my research group (e.g. Computer Methods in Applied Mechanics and Engineering [PDF1][PDF2][PDF3][URL], Journal of Engineering Mechanics [PDF], International Journal for Numerical Methods in Engineering [PDF] and International Journal of Analytical and Numerical Methods in Geomechanics [PDF]). Co-authoring a manuscript can provide valuable insights on the quality of the collaborations for both the PI and the students. This knowledge can help adjusting the strategies to ensure successful mentorship. All group members, including myself, must uphold the highest standards of rigor and integrity. I encourage everyone to plan research activities by balancing risk and reward. Often, groundbreaking work requires stepping away from conventional approaches; however, there is no value in novelty for its own sake. What often distinguishes excellent researchers from good ones is the ability to calculate and manage risk, devise plans, and execute them so that the chances of asking the right questions — and finding correct answers — are maximized.
Day-to-day logistics
An effective advisor should develop the ability of the students to become independent thinkers who can choose important problems and formulate plans to maximize the desirable outcome at the right time and place. For PhD students and postdocs, my aims are to identify a theme that (i) excites both of us, (ii) matches the student’s competencies, personality, and work habits, (iii) contains elements of fundamental importance, and (iv) has reasonable prospects for sustainable funding during — and ideally beyond — the PhD. As your advisor, my primary duties are to:
My goal is to help you do your best work and to keep you focused, motivated, and funded. There are three major channels of communication used in my research group for different purposes. The most important form of communication is the one-on-one meeting and co-authoring the papers (often in Overleaf). This close collaboration gives me a window to observe not just the students' preparedness of subjects, but also work ethnics, intellectual curiosity, communication skills and their enthusiasms on the assigned research activities. The team members, meanwhile, also have the firsthand experience to engage on the research topics. The second form of communication is the biweekly meeting where members present their latest reasons. The objective of the bi-weekly meeting is to exchange ideas among team members. I also use this opportunity to discuss logistics, funding plans and other developments that could have impacts on the team members. To speed up communication, I also communicate with my students using Discord. The Discord is used exclusively for developing/exploring research ideas and have a short-term close communications while revising manuscripts, presentations and other items that require a brief supervision. In all three channels, I will use the opportunities to give my informal feedback and assessment periodically. Meanwhile an annual assessment in writing will also be provided.
If, after given a reasonable time and effort, the research is not fruitful, I will make an adjustment based on the evidence I gathered as swiftly as possible. In such a scenario, the first primary objective is to assess the situation objectively and make a productive and practical adjustment to prevent a deadlock and prevent the situations worsen over time. We will evaluate the pros and cons of all feasible options. For instance, the research scope can be amended or abandoned; new researchers/collaborators with complementary skill sets can be assigned to cover the research; priority of the scope can be changed. Meanwhile, It is also possible that the best cause of action is to neglect the noise and stay push. In all different scenarios, it is not possible to guarantee that all the decisions are correct, but they should be made as rationally and as timely as possible.
An effective advisor should develop the ability of the students to become independent thinkers who can choose important problems and formulate plans to maximize the desirable outcome at the right time and place. For PhD students and postdocs, my aims are to identify a theme that (i) excites both of us, (ii) matches the student’s competencies, personality, and work habits, (iii) contains elements of fundamental importance, and (iv) has reasonable prospects for sustainable funding during — and ideally beyond — the PhD. As your advisor, my primary duties are to:
- Provide an intellectually stimulating and safe environment for meaningful research.
- Motivate you to set and uphold high standards for your work.
- Offer nuclei of research ideas and define them as precisely as possible.
- Help you pursue research ideas efficiently.
- Help you evaluate setbacks and develop plans to address research challenges.
- Evaluate your intellectual growth objectively.
My goal is to help you do your best work and to keep you focused, motivated, and funded. There are three major channels of communication used in my research group for different purposes. The most important form of communication is the one-on-one meeting and co-authoring the papers (often in Overleaf). This close collaboration gives me a window to observe not just the students' preparedness of subjects, but also work ethnics, intellectual curiosity, communication skills and their enthusiasms on the assigned research activities. The team members, meanwhile, also have the firsthand experience to engage on the research topics. The second form of communication is the biweekly meeting where members present their latest reasons. The objective of the bi-weekly meeting is to exchange ideas among team members. I also use this opportunity to discuss logistics, funding plans and other developments that could have impacts on the team members. To speed up communication, I also communicate with my students using Discord. The Discord is used exclusively for developing/exploring research ideas and have a short-term close communications while revising manuscripts, presentations and other items that require a brief supervision. In all three channels, I will use the opportunities to give my informal feedback and assessment periodically. Meanwhile an annual assessment in writing will also be provided.
If, after given a reasonable time and effort, the research is not fruitful, I will make an adjustment based on the evidence I gathered as swiftly as possible. In such a scenario, the first primary objective is to assess the situation objectively and make a productive and practical adjustment to prevent a deadlock and prevent the situations worsen over time. We will evaluate the pros and cons of all feasible options. For instance, the research scope can be amended or abandoned; new researchers/collaborators with complementary skill sets can be assigned to cover the research; priority of the scope can be changed. Meanwhile, It is also possible that the best cause of action is to neglect the noise and stay push. In all different scenarios, it is not possible to guarantee that all the decisions are correct, but they should be made as rationally and as timely as possible.
Empirical observations on traits and habits of successful team members
There are straightforward habits that increase your odds of making important progress: protect your sleep, eat well, and exercise regularly. Develop disciplined practices such as arriving at group meetings fully prepared, keeping a research journal to ensure reproducibility, paying attention to detail, and being scrupulously honest when analyzing data and interpreting results. These habits may seem trivial, but they compound into large advantages over time and shape the trajectory of a career.
There are traits I observed consistently in students/team members who are more successful than the others. They tend to be more curious and excited for knowledge and more open-mind to try/learn new things. They think more precisely and proactively, invest time more wisely and care less about impressing others for its own sake. They do not have the habits of doing the bare minimum just to “get by or cutting corners whenever not getting caught. The opposite is also true.
Resources
Columbia has a work/life balance that provides general resources to help students and postdoc to pursuit meaningful and productive academic, personal and work lives. These services ranges from counseling, student-life support groups to off-campus housing.For more information please visit: https://worklife.columbia.edu/ Columbia graduate student are unionized.
There are straightforward habits that increase your odds of making important progress: protect your sleep, eat well, and exercise regularly. Develop disciplined practices such as arriving at group meetings fully prepared, keeping a research journal to ensure reproducibility, paying attention to detail, and being scrupulously honest when analyzing data and interpreting results. These habits may seem trivial, but they compound into large advantages over time and shape the trajectory of a career.
There are traits I observed consistently in students/team members who are more successful than the others. They tend to be more curious and excited for knowledge and more open-mind to try/learn new things. They think more precisely and proactively, invest time more wisely and care less about impressing others for its own sake. They do not have the habits of doing the bare minimum just to “get by or cutting corners whenever not getting caught. The opposite is also true.
Resources
Columbia has a work/life balance that provides general resources to help students and postdoc to pursuit meaningful and productive academic, personal and work lives. These services ranges from counseling, student-life support groups to off-campus housing.For more information please visit: https://worklife.columbia.edu/ Columbia graduate student are unionized.
Visiting scholars
If you are interested in visiting my research group temporarily (with external support), please contact me at least a few months ahead of your proposed arrival date. Visiting scholars must provide evidence that they possess sufficient communication skills and have sufficient support to apply for a US visa. Only researchers with compatible research interests and sufficient research background will be considered. We do not support visiting researchers coming to New York for leisure travel. Interested candidate please contact me by email and fill out the application form available at https://portal.seas.columbia.edu/form/view.php?id=114.
If you are interested in visiting my research group temporarily (with external support), please contact me at least a few months ahead of your proposed arrival date. Visiting scholars must provide evidence that they possess sufficient communication skills and have sufficient support to apply for a US visa. Only researchers with compatible research interests and sufficient research background will be considered. We do not support visiting researchers coming to New York for leisure travel. Interested candidate please contact me by email and fill out the application form available at https://portal.seas.columbia.edu/form/view.php?id=114.