...These short walks lasted about three hours and gave us a great chance to spend time outdoors, get to know each other, and exchange ideas about our research and the courses. Overall, this summer school was a valuable chance to learn new mathematics and meet other young researchers. I am grateful for the opportunities to exchange ideas...The courses were very well-organized and there were many opportunities to talk with other students and professors....

This was the most rewarding part for me. Between lectures, there was a half-hour tea break, and every afternoon was reserved for open discussion—...Participants came from all over the world (for example, one student completed a music degree in Russia before returning to the U.S. to study mathematics—so cool!) Because the topics spanned optimal transport, PDEs, probability, optimization, machine learning, statistics, and SDEs, everyone approached problems from very different angles, and I thoroughly enjoyed that vibrant, collaborative atmosphere. I found these interactions to be immensely beneficial for my own understanding and growth. Another highlight was getting advice from the more senior participants....I picked their brains about graduate-school applications and which programs to consider—originally I had only planned to apply in the U.S., but current policy uncertainty has prompted me to develop backup options as well. I also had especially deep conversations with two students... I felt humbled by their dedication..... “The foremost objective of this summer school is to create a dynamic learning environment that unites students from diverse backgrounds such as PDE theory, probability, or optimal transport.” I believe SLMath achieved this perfectly.

參與人員為來自世界各地的博士生及碩士生,課程內容皆是關於極地氣候、極地生態等,具體上就是介紹如何結合實地勘查結果及資料來進行不同方式的建模研究,使用到的數學工具更是琳瑯滿目,例如:微分方程、機率及隨機變數、離散數學及圖論等,對於數學模型所給出的數學結果也都有生物意義上的解釋及現實生活中的現象與之對應。此外教授們也曾經乘坐破冰船,在北極與南極進行過實地研究,再加上他們生動有趣的授課方式,將所親身經歷的種種分享得活靈活現,並且由於阿拉斯加大學費爾班克斯分校處於近北極圈的地理位置,從而在校內有許多在極地勘查時所需要的研究工具,我們除了聽課之外,也有去到他們的校內實驗室參觀實驗器材,觀賞他們是如何實際研究海冰。....

...Personally, I found the first week's lectures more aligned with my background and interests. The exploration of different symbol spaces and elliptic/semi-Fredholm estimates sparked intriguing ideas. Also, the diverse focus of students—some more familiar with analytical tools, others with PDE results—enriched our discussions. Outside of class, June 19th Juneteenth, which is a U.S. holiday, and the weekend providing free time we can visit san Francisco or near city. On the second Wednesday afternoon, we visited SLMath for a tour. Finally, on the last evening, we enjoyed dinner at the school pub.

...The exercises were usually easier than the lecture material, mostly involving working out a few examples....Throughout the process, everyone was very patient no matter who asked even the most basic questions, others would carefully explain. I believe our department should learn from this kind of atmosphere....Each activity gave me the chance to meet new people as well as become closer with friends I already knew....Later, we even created an extra group where we talked about wanting to join another summer school together in the future.

...它們不僅展現了組合數學的結構之美,也提供了我對理論計算機科學研究具啟發性的洞見,幫助我認識兩者之間的聯繫。在每門課的習題討論中,我得以與來自世界各地的博士生深入交流,分享不同的解題思路與研究經驗,並從中獲得了許多新想法。此外,各類學術演講、經驗分享會與非正式交流活動,讓我對整個組合數學領域的研究生態與國際合作氛圍有了更立體的理解,也擴展了在這個圈子的人脈以及與外國學者的交友經驗,更加確立了自己投身該領域研究的志向。...這次參與 PCMI 對我而言是一段極為寶貴且收穫豐富的經歷,無論在專業知識、研究能力、學術視野還是人脈方面,都感受到明顯的提升,也讓我更明確地確立了未來的研究方向。...

2024 心得分享

學生: 蕭明，梁孟豪，蔡以心，陳嵩昀，李秉鴻，林芮吟，許嘉麟，李永丞